
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]


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Given the sequence $\{a\_n\}$ with the sum of its first $n$ terms $S\_n=2^{n}+a$,

(1) Find the general term formula for $\{a\_n\}$ when $a=1$.

(2) If the sequence $\{a\_n\}$ is a geometric sequence, find the value of $a$.

(3) Under the condition of (2), find the sum of $a\_1^{2}+a\_2^{2}+a\_3^{2}+…+a\_n^{2}$.

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