
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
Suppose that  $a_0=1$  and that  $a_{n+1}=a_n+e^{-a_n}$  for  $n=0,1,2,\dots.$  Does  $a_n-\log n$  have a finite limit as  $n\to\infty?$  (Here  $\log n=\log_en=\ln n.$ )

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