
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 special $24$-hour digital clock operates with a fault: every time it should display the digit $2$, it instead shows an $8$. For instance, when the correct time is 2:30 AM, the clock mistakenly shows 8:30 AM. What fraction of the day does the clock display the correct time?

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