
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 $\left\{x_{n}\right\}$ where $x_{1}=2$ and $x_{2}=3$, and it satisfies the following conditions:
$$
\left\{\begin{array}{l}
x_{2m+1}=x_{2m}+x_{2m-1}, \quad m \geq 1, \\
x_{2m}=x_{2m-1}+2x_{2m-2}, \quad m \geq 2 .
\end{array}\right.
$$

Find the general term formula for the sequence $\left\{x_{n}\right\}$.


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