
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
In the sequence $\{a_{n}\}$, for any $n\in \mathbb{N}^{*}$, $a_{n}=k$ if and only if $2^{k}\leqslant n \lt 2^{k+1}$, where $k\in \mathbb{N}$. If it satisfies $a_{m}+a_{2m}+a_{4m}+a_{8m}+a_{16m}\geqslant 52$, then the smallest value of $m$ is ____.

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