
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In an archery contest, the two contestants A and B start at \( x = 0 \) and walk towards the target at \( x = 1 \) together. Each chooses the distance from which they shoot. A has a probability \( x^2 \) of hitting the target from \( x \). B has a probability \( x \) of hitting the target from \( x \). If both hit the target, then the first to shoot wins. What is A's best strategy?

Present the answer in LaTex format: \boxed{Your answer}
user