
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
1. Evaluate the expression $\sin (-120^{\circ})\cos 210^{\circ}+\cos (-300^{\circ})\sin (-330^{\circ})$.
2. Given the function $f (α)= \dfrac{2\sin (π+α)\cos (π-α)-\cos (π+α)}{1+\sin ^{2}α+\cos \left( \frac{3π}{2}+α \right)-\sin ^{2}\left( \frac{π}{2}+α \right)}(1+2\sin α\neq 0)$, find the value of $f\left( -\frac{23π}{6} \right)$.

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