
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
Simplify $f(\alpha)$ to its simplest form and solve for $\sin^2\alpha - \sin\alpha\cos\alpha - 2\cos^2\alpha$ when $f(\alpha) = -2$.

Given: $f(\alpha)= \dfrac {\sin (2\pi-\alpha)\cos (\pi+\alpha)\cos ( \dfrac {\pi}{2}+\alpha)\cos ( \dfrac {\pi}{2}-\alpha)}{\cos (\pi -\alpha )\sin (3\pi -\alpha )\sin (-\alpha )\sin ( \dfrac {\pi}{2}+\alpha )}$

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