
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
Let  $a_n\ (n\geq 1)$  be the value for which  $\int_x^{2x} e^{-t^n}dt\ (x\geq 0)$  is maximal. Find  $\lim_{n\to\infty} \ln a_n.$ 

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