
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 the equation $a_n^2 = 4S_n - 2a_n - 1 (n\in \mathbf{N}^*)$, where $S_n$ denotes the sum of the first $n$ terms of the sequence.

(I) Find the values of $a_1$ and $a_2$;

(II) Find the general term formula of the sequence.

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