
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 the function $f(\alpha) = \frac {\sin(2\pi-\alpha)\cos(\pi+\alpha)\cos\left(\frac {\pi}{2}-\alpha\right)\cos\left(\frac {11\pi}{2}-\alpha\right)}{\sin(3\pi -\alpha )\cos\left(\frac {\pi}{2}+\alpha\right)\sin\left(\frac {9\pi}{2}+\alpha\right)} + \cos(2\pi-\alpha).$
(1) Simplify $f(\alpha)$.
(2) If $f(\alpha) = \frac{\sqrt{10}}{5},$ find the value of $\frac{1}{\sin\alpha} + \frac{1}{\cos\alpha}.$

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