
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
Given that $α$ is an angle in the third quadrant and $f(α)= \frac{\tan (π -a)\cos (2π -a)\sin (-a+\frac{3π }{2})}{\cos (-a-π )\tan (-π -a)}$.

(1) Simplify $f(α)$;

(2) If $\cos (a-\frac{3π }{2})= \frac{1}{5}$, find the value of $f(a)$;

(3) If $α=-1860^{\circ}$, find the value of $f(α)$.

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