
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

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

have two distinct roots, the sum of the squares of which is less than 1?

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