
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
The sequence $\left\{a_{n}\right\}$ is defined as follows:
$$
a_{1}=2, a_{2}=3,\left\{\begin{array}{l}
a_{2m+1}=a_{2m}+a_{2m-1} \quad (m \geq 1), \\
a_{2m}=a_{2m-1}+2a_{2m-2} \quad (m \geq 2),
\end{array}\right.
$$
Find $a_{n}$.

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