
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
$$f(α)= \frac {\sin(π-α)\cos(2π-α)\sin(-α+ \frac {3π}{2})}{\sin( \frac {π}{2}+\alpha )\sin(-π -\alpha )}.$$
(1) Simplify $f(α)$.
(2) If $α$ is an angle in the third quadrant and $\cos\left(α+ \frac {π}{3}\right) = \frac {3}{5}$, find the value of $f(α)$.

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