
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 a geometric sequence {\(a_n\)}, where \(a_5 + a_7 = \int_{-2}^{2} \sqrt{4-x^2}dx\), find the value of \(a_6(a_4 + 2a_6 + a_8)\).

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