
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
Two sequences \(\{a_n\}\) and \(\{b_n\}\) satisfy \(a_1 = 2\), \(b_1 = 1\), \(a_{n+1} = 5a_n + 3b_n + 7\), and \(b_{n+1} = 3a_n + 5b_n\) (where \(n \in \mathbf{N}_+\)). Then the general term of the sequence \(\{a_n\}\) is \(a_n = \qquad\).

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