
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 \( y = 10 \tan \left[(2k-1) \frac{x}{5}\right] \quad \left(k \in \mathbf{Z}^{+}\right) \), determine the smallest positive integer value of \( k \) such that when \( x \) varies between any two consecutive integers (including the integers themselves), the function loses its meaning at least twice.

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