
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
Let the function \( f(x) = \left\{
\begin{array}{ll}
\frac{1}{p} & \text{if } x = \frac{q}{p}, \\
0 & \text{if } x \neq \frac{q}{p},
\end{array}
\right. \)
where \( p \) and \( q \) are coprime (i.e., relatively prime) and \( p \geq 2 \). Determine the number of values of \( x \) in the interval \([0,1]\) for which \( f(x) > \frac{1}{5} \).

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