The Dragon and the Poisonous Wells on the Mountain

Scenario

On a mountain, there are 7 poisonous wells numbered 1 to 7 in strictly increasing order of elevation and potency. Poison $j$ is more potent than poison $i$ if $j > i$. Antidote Rule: The only way to neutralize poison $k$ is to subsequently drink from a strictly stronger well (Well $> k$). Drinking a stronger poison completely cures and neutralizes all previously consumed weaker poisons. Well 7 is at the mountain's summit. No well $> 7$ exists; drinking from Well 7 without later drinking a stronger poison is fatal. A Knight and a Dragon engage in a duel:

1. Each brings a cup of liquid for the opponent to drink.
2. Both drink the liquid given to them.
3. Immediately following, both are free to run to any wells on the mountain and drink.

Your Task

1. Devise the Knight's winning strategy that guarantees his survival while ensuring the Dragon dies.
2. Detail the exact actions taken by the Knight before, during, and after the duel.
3. Explain why the Dragon's optimal response cannot prevent this outcome.

Constraints

• Both players are rational and know the rules of the wells.

Examples If the Knight brings Well 7 poison, he himself must have drunk it (or had no cure), which is fatal. Bringing ordinary water exploits the Dragon's rush to Well 7.