
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
The numerical sequence \(\left\{a_{n}\right\}_{n=1}^{\infty}\) is defined such that \(a_{1}=\log _{2}\left(\log _{2} f(2)\right)\), \(a_{2}=\log _{2}\left(\log _{2} f(f(2))\right)\), \(\ldots, a_{n}=\log _{2}(\log _{2} \underbrace{f(f(\ldots f}_{n}(2)))), \ldots\), where \(f(x)=x^{x}\). Determine the number \(n\) for which \(a_{n}=2059+2^{2059}\).

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