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When considering which action would not lead to the termination of an offer, requesting more time for acceptance by the offeree is significant. This request does not inherently alter or negate the original offer but rather indicates the offeree's desire to evaluate the offer before making a final decision. The offeree is essentially seeking to keep the offer open for a specified period, which does not terminate the original terms.

In a typical contractual scenario, offers can be revoked by the offeror at any time before acceptance, meaning that such revocation would terminate the offer. A counter-offer, such as an acceptance that is contingent upon a change in price, would also effectively terminate the original offer since it proposes a new set of terms. Furthermore, the death of the offeror would terminate the offer automatically, as the offer is personal to the parties involved.

Thus, the action of requesting more time doesn't actually end the negotiation process but instead allows for continued consideration of the offer at hand.