
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 $a$, let $\left[a\right]$ denote the largest integer not exceeding $a$. For example, $\left[4\right]=4$, $[\sqrt{3}]=1$. Now, for the number $72$, the following operations are performed: $72\stackrel{1st}{→}[\sqrt{72}]=8\stackrel{2nd}{→}[\sqrt{8}]=2\stackrel{3rd}{→}[\sqrt{2}]=1$. In this way, the number $72$ becomes $1$ after $3$ operations. Similarly, among all positive integers that become $2$ after $3$ operations, the largest one is ____.

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