In this sentence

①assume sth / assume (that)...v.假定；设想

Synonymspresume, suppose, take for granted

原句中“assume the other side's intentions”为及物动词接名词宾语，表示在缺乏确凿证据的情况下，想当然地“臆断、假定”对方的意图。

• Never assume that every critic is a cynic.绝不要假定每一个批评者都是愤世嫉俗的人。— Norman Cousins

②assume control / responsibility / powerv.承担；担任

Synonymstake on, undertake, shoulder

• You must assume responsibility for your own life and happiness.你必须对自己的生活和幸福承担责任。

③assume an air / look / rolev.装出；假装

Synonymsfeign, affect, put on

• Assume a virtue, if you have it not.即使你没有某种美德，也要装出有的样子。— William Shakespeare

In this sentence

①an assumption that / make an assumptionn.假定；设想

Synonymspresumption, supposition, premise, hypothesis

句中紧接前文的动词 assume，作 tests 的宾语，指在缺乏确凿证据前主观认定的想法或假设，属于可数名词用法。

• Your assumptions are your windows on the world. Scrub them off every once in a while, or the light won't come in.你的假设是你观察世界的窗户。偶尔擦拭它们，否则光芒就无法照进来。— Isaac Asimov

②assumption of sthn.承担；担任（权力、责任等）

Synonymsacquisition, taking on, shouldering

• With the assumption of power comes the duty to serve something greater than oneself.权力的承担伴随着服务于比自身更崇高事物的责任。

In this sentence

①assure sbv.使放心；使安心

Synonymsreassure, comfort, soothe

句中接人作宾语（both parties 指代谈判双方），省略了 assurance 的具体内容，意为通过核实假设来消除双方疑虑，让彼此都安心。

• Nothing can bring you peace but yourself; nothing can assure you but the triumph of principles.除了你自己，没有任何事物能带给你平静；除了原则的胜利，没有任何事物能让你安心。

②assure sb that...v.向某人保证；使某人确信

Synonymspromise, convince, guarantee

• History assures us that all great movements began in the conviction of a single individual.历史向我们证实，所有伟大的运动最初都始于某个个体的坚定信念。

③assure sb of sthv.向某人确保某事；使某人对某事确信

Synonymsreassure, pledge, swear

• I assure you of my profound respect and constant readiness to serve the cause of justice.我向您确保我的由衷敬意，以及随时准备为正义事业效力的决心。

④assure sthv.确保；使必然发生

Synonymsensure, guarantee, secure

• To be prepared for war is one of the most effectual means of preserving peace and assuring liberty.居安思危是维护和平与确保自由最有效的手段之一。

①ensure that ...v.确保；保证（某事发生）

Synonymsmake sure, guarantee, certify

• To ensure that you hit the target, shoot first and, whatever you hit, call it the target.要想确保击中目标，先开枪，然后把打中的任何东西都称作目标。— Ashleigh Brilliant

②ensure sthv.保障；使……必然发生

Synonymssecure, guarantee, assure

• Those who prepare for all the emergencies of life beforehand may equip themselves at the expense of joy, and ensure their defeat.那些事先为生活中一切突发事件做好准备的人，可能会以牺牲快乐为代价武装自己，从而注定失败。— Arthur Christopher Benson

③ensure sb sthv.为某人确保/赢得（某事物）

Synonymssecure, guarantee, gain

• Excellence in small things will ensure you greatness in large things.在小事上做到极致，必将为你赢得伟大的成就。

①insure sth (against sth)v.给……投保；承保

Synonymsunderwrite, cover, protect

• We insure our houses against fire, but we leave our minds unprotected against the flames of anger.我们为房屋投保以防火灾，却任由心灵在愤怒的烈火中毫无防备。

②insure sb/sth (for sth)v.为……买保险（设定保额）

Synonymscover, warrant

• You can insure a diamond for millions, but the eye that beholds its beauty remains priceless.你可以为一颗钻石投保数百万，但注视其美丽的那双眼睛却始终无价。

③insure that / insure against sthv.确保；防范（多见于美式英语，同 ensure）

Synonymsensure, guarantee, secure

• One of the best ways to insure future happiness is to be as happy as is rightfully possible today.确保未来幸福的最佳途径之一，就是在今天尽情享受合情合理的快乐。— Charles William Eliot