
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 a real number $a > 0$, which satisfies the following conditions:
1. There exists $x \in \mathbb{R}$ such that $|\sin x| > a$ has a solution.
2. For all $x \in \left[\frac{\pi}{4}, \frac{3\pi}{4}\right]$, $\sin^2 x + a\sin x - 1 \geq 0$.

Determine the range of values for the real number $a$.

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