
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
Let \( u_n \) be the sequence defined by \( u_1 = 4 \), \( u_2 = 9 \), and subsequently \( u_n = 3u_{n-1} - u_{n-2} - 2 \cdot (-1)^n \). Find \( u_n \).

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