
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 \( a \) for which the quadratic trinomials \( x^{2} - 6x + 4a \) and \( x^{2} + ax + 6 \) each have two roots, with the sum of the squares of the roots of the first trinomial equal to the sum of the squares of the roots of the second trinomial.

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