
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
Given that the sequence $\{a_n\}$ is a geometric sequence and the sequence $\{b_n\}$ is an arithmetic sequence, if $a_1 \cdot a_5 \cdot a_9 = -8$ and $b_2 + b_5 + b_8 = 6\pi$, find the value of $$\cos \left( \frac{b_4 + b_6}{1 - a_3 \cdot a_7} \right)$$

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