
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
Solve the recurrence relation:
$$
\left\{\begin{array}{l}
a_{n}=5a_{n-1}-6a_{n-2}+n+2 \quad (n \geq 2), \\
a_{0}=\frac{27}{4}, \quad a_{1}=\frac{49}{4}.
\end{array}\right.
$$

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