
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 geometric sequence $\{a_n\}$, it is known that for any positive integer $n$, the sum $a_1+a_2+a_3+\ldots+a_n = 2^n + m$. Find the value of $a_1^2+a_2^2+a_3^2+\ldots+a_n^2$.

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