
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 $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$ satisfy $a_{1}=2, b_{1}=1$, and the recurrence relations $\left\{\begin{array}{l}a_{n+1}=5a_{n}+3b_{n}+7 \\ b_{n+1}=3a_{n}+5b_{n}\end{array} \quad \left(n \in \mathbf{N}^{*}\right)\right.$. Find their general term formulas: $a_{n}=$ $\qquad$ $b_{n}=$ $\qquad$ .

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