
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 $f(\alpha)= \dfrac {\sin ( \dfrac {\pi}{2}-\alpha)\cos (10\pi-\alpha)\tan (-\alpha+3\pi)}{\tan (\pi+\alpha)\sin ( \dfrac {5\pi}{2}+\alpha)}$.
  1. Simplify $f(\alpha)$;
  2. If $\alpha=-1860^{\circ}$, find the value of $f(\alpha)$;
  3. If $\alpha\in(0, \dfrac {\pi}{2})$, and $\sin (\alpha- \dfrac {\pi}{6})= \dfrac {1}{3}$, find the value of $f(\alpha)$.

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