
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 \(AC\), \(BC\), \(BS\), \(AS\) of the regular triangular pyramid \(SABC\) with vertex \(S\), points \(K\), \(L\), \(M\), \(N\) are chosen, respectively. It is known that the points \(K\), \(L\), \(M\), \(N\) lie in one plane, and \(KL = MN = 2\), \(KN = LM = 18\). In the quadrilateral \(KLMN\), there are two circles \(\Omega_1\) and \(\Omega_2\), where circle \(\Omega_1\) is tangent to sides \(KN\), \(KL\), and \(LM\), and circle \(\Omega_2\) is tangent to sides \(KN\), \(LM\), and \(MN\). The straight circular cones \(\mathcal{F}_1\) and \(\mathcal{F}_2\) with bases \(\Omega_1\) and \(\Omega_2\), respectively, are located inside the given pyramid, where the vertex \(P\) of cone \(\mathcal{F}_1\) lies on edge \(AB\), and the vertex \(Q\) of cone \(\mathcal{F}_2\) lies on edge \(CS\).

a) Find \(\angle SAB\).

b) Find the length of segment \(CQ\).

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