
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
For which values of the parameter \( a \) does the equation

$$
\log _{2}\left(2 x^{2}+(2 a+1) x-2 a\right)-2 \log _{4}\left(x^{2}+3 a x+2 a^{2}\right)=0
$$

have two distinct roots, the sum of the squares of which is greater than 4?

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