
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
The number \(s\) can be expressed as a four-place decimal \(0.wxyz\), where \(w, x, y,\) and \(z\) represent digits. It is desired to approximate \(s\) by a fraction whose numerator is 1 or 2 and whose denominator is an integer. The closest such fraction to \(s\) is \(\frac{1}{5}\). What is the number of possible values for \(s\)?

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