
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
A survey was conducted by a mischievous student regarding the weekend activities of their classmates. Of the class, $\frac{5}{13}$ went out for fun, $\frac{4}{13}$ participated in youth palace activities, and the rest stayed at home. What fraction of the students stayed at home?

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