
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
Suppose $(v_n)$ is a sequence of real numbers satisfying
\[ v_{n+2} = 2v_{n+1} + v_{n} \]
with $v_4 = 15$ and $v_7 = 255$. Find $v_5$.

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