
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, any of which could be zero. 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 \( \frac{1}{4} \). What is the number of possible values for \( s \)?

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