
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
Given the following expression:

$$
y = x^{2} - (8a - 2)x + 15a^{2} - 2a - 7
$$

1. Determine the value of \(a\) so that this expression is positive for all values of \(a\).
2. Determine the value of \(a\) so that the sum of the squares of the roots of the equation \(y = 0\) is 24.

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