
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 an arithmetic sequence \\(\left\{ a_n \right\}\\) with the first term \\(a\\) and common difference \\(b\\), and a geometric sequence \\(\left\{ b_n \right\}\\) with the first term \\(b\\) and common ratio \\(a\\), where \\(a,b\\) are positive integers greater than \\(1\\), and \\(a_1 < b_1, b_2 < a_3\\). For any \\(n \in \mathbb{N}^*\), there always exists \\(m \in \mathbb{N}^*\) such that \\(a_m + 3 = b_n\\) holds. Find the general term of \\(\left\{ a_n \right\}\\).

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