
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 sequences $\{a_n\}$ and $\{b_n\}$ satisfy the following relations: $a_n = 5a_{n-1} - 6b_{n-1}$, $b_n = 3a_{n-1} - 4b_{n-1}$, and $a_1 = a$, $b_1 = b$. Find the general terms $a_n$ and $b_n$.

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