
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
Let the distance from point \( P \) to plane \( \alpha \) be \( \sqrt{3} \). Point \( Q \) is on plane \( \alpha \) such that the angle between line \( PQ \) and plane \( \alpha \) is no less than \( 30^\circ \) and no greater than \( 60^\circ \). The area of the region formed by such points \( Q \) is \(\qquad\)

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