
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
If the fraction \(\frac{p}{q}\) (where \( p, q \in \mathbf{Z}_{+} \)) is converted into a decimal as
\[
\frac{p}{q} = 0.198 \cdots,
\]
then, when \( q \) takes its minimum value, what is \( p+q \)?

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