
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
Consider a sequence of real numbers $(v_n)$ defined by the recursive relation
\[ v_{n+2} = 3v_{n+1} - 2v_n \]
Given that $v_4 = 6$ and $v_7 = 87$, find $v_6$.

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