
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
For any real number $x$, we define $\lceil X \rceil$ as the smallest integer greater than $x$. For example, $\lceil 4 \rceil = 5$, $\lceil \sqrt{3} \rceil = 2$, $\lceil -2.5 \rceil = -2$. Perform the following operations on $64$:
$$64 \xrightarrow{\text{1st}} \lceil \sqrt{64} \rceil = 9 \xrightarrow{\text{2nd}} \lceil \sqrt{9} \rceil = 4 \xrightarrow{\text{3rd}} \lceil \sqrt{4} \rceil = 3 \xrightarrow{\text{4th}} \lceil \lceil \sqrt{3} \rceil \rceil = 2$$
Thus, after $4$ operations, $64$ becomes $2$. Among all positive integers that also become $2$ after $4$ operations, find the largest one.

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