
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 general term formula of the sequence $\{a_n\}$ is $a_n=2^{n-1}$. Find the maximum value of $n$ that makes the inequality $a_1^2+a_2^2+…+a_n^2 < 5 \times 2^{n+1}$ hold.

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