
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
Given a sequence $\{a\_n\}$ where all terms are positive numbers and it satisfies $a\_n^{2}=4S\_n-2a\_n-1 (n∈N^{})$, where $S\_n$ is the sum of the first $n$ terms of the sequence.

1. Find the values of $a\_1$ and $a\_2$.
2. Find the general term formula for the sequence $\{a\_n\}$.

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