
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
In the region D: $$\begin{cases} \overset{-1\leq x\leq 1}{0\leq y\leq 1}\end{cases}$$, a point P(x, y) is randomly chosen. The probability that this point satisfies the inequality $y \leq x^2$ is $a$. Then, the coefficient of $x^2$ in the expansion of the binomial $\left( \frac{x}{a} - \frac{1}{\sqrt{x}} \right)^5$ is ______.

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