
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
\[ \log _{a} \sqrt{4+x} + 3 \log _{a^{2}}(4-x) - \log _{a^{4}}\left(16-x^{2}\right)^{2} = 2 \]
For which values of \(a\) does the equation have a solution?

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