
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
Define the sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$ as follows:
$$
\begin{array}{l}
a_{1}=b_{1}=1, \quad a_{2}=2, \quad b_{2}=7, \\
a_{n+2}=4a_{n+1}-a_{n}, \quad b_{n+2}=6b_{n+1}-b_{n} \quad (n \in \mathbf{Z}_{+}).
\end{array}
$$

Find all the common terms of the sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$.

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