
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 angle $a$ is a third-quadrant angle, and let $f(a) = \frac{\sin(\pi - a) \sin(a) \cos(\pi + a)}{\sin(\frac{\pi}{2} - a) \cos(a + \frac{\pi}{2}) \tan(-a)}$.

(Ⅰ) Simplify $f(a)$.

(Ⅱ) If $\sin(2\pi - a) = \frac{1}{5}$, find the value of $f(a)$.

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