
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 two sequences \\({a\_n}\\) and \\({b\_n}\\), where all terms are positive, they satisfy the following conditions: \\({a\_n}, {b\_n}, {a\_{n+1}}\\) form an arithmetic sequence, \\({b\_n}, {a\_{n+1}}, {b\_{n+1}}\\) form a geometric sequence, and \\(a\_1=1\\), \\(a\_2=3\\). Find the general term formula for the sequence \\({a\_n}\\).

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