
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 proposition p: $x_1$ and $x_2$ are the two real roots of the equation $x^2 - mx - 2 = 0$, the inequality $a^2 - 5a - 3 \geq |x_1 - x_2|$ holds for any real number $m \in [-1, 1]$; proposition q: the inequality $ax^2 + 2x - 1 > 0$ has solutions. If proposition p is true and proposition q is false, find the range of values for $a$.

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