
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
A function  $f$  from the positive integers to the nonnegative integers is defined recursively by  $f(1) = 0$  and  $f(n+1) = 2^{f(n)}$  for every positive integer  $n$ .  What is the smallest  $n$  such that  $f(n)$  exceeds the number of atoms in the observable universe (approximately  $10^{80}$ )?

*Proposed by Evan Chen*

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