
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
Find all values of the parameter \(a\) for which the equation \[
\left(\left(1-x^{2}\right)^{2}+2 a^{2}+5 a\right)^{7}-\left((3 a+2)\left(1-x^{2}\right)+3\right)^{7}=5-2 a-(3 a+2) x^{2}-2 a^{2}-\left(1-x^{2}\right)^{2}
\] has two distinct solutions on the interval \(\left[-\frac{\sqrt{6}}{2} ; \sqrt{2}\right]\). Indicate these solutions for each found \(a\).

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