
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
Given that a $12$-hour digital clock displays the wrong numbers for '1' and '2', showing '9' and '8' respectively, determine the fraction of the day that the clock will show the correct time.

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