
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
On the edges \( A C, B C, B S, A S \) of a regular triangular pyramid \( S A B C \) with vertex \( S \), points \( K, L, M, N \) are selected, respectively. It is known that points \( K, L, M, N \) lie in the same plane, and \( K L = M N = 4 \), \( K N = L M = 9 \). In the quadrilateral \( K L M N \), there are two circles \( \Omega_{1} \) and \( \Omega_{2} \), with circle \( \Omega_{1} \) tangent to sides \( K N, K L \), and \( L M \), and circle \( \Omega_{2} \) tangent to sides \( K N, L M \), and \( M N \). The right circular cones \( \mathcal{F}_{1} \) and \( \mathcal{F}_{2} \) with bases \( \Omega_{1} \) and \( \Omega_{2} \), respectively, are located inside the given pyramid, with the vertex \( P \) of cone \( \mathcal{F}_{1} \) lying on edge \( A B \) and the vertex \( Q \) of cone \( \mathcal{F}_{2} \) lying on edge \( C S \).

a) Find \( \angle S A B \).

b) Find the length of segment \( C Q \).

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