
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 $\alpha = 2k\pi - \frac{\pi}{5} (k \in \mathbb{Z})$, if angle $\theta$ has the same terminal side as angle $\alpha$, determine the value of $y= \frac{\sin \theta}{|\sin \theta|}+ \frac{\cos \theta}{|\cos \theta|}+ \frac{\tan \theta}{|\tan \theta|}$.

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