
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 an angle \( A \) equal to \( \alpha \), a circle is inscribed, touching its sides at points \( B \) and \( C \). A line, tangent to the circle at some point \( M \), intersects the segments \( A B \) and \( A C \) at points \( P \) and \( Q \) respectively. For which \( \alpha \) can the inequality \( S_{PAQ} < S_{BMC} \) hold?

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