
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 24-hour digital clock is designed to display the hour and minute of the day. However, there is a glitch: every time it is supposed to display a '2', it mistakenly shows a '7'. For instance, when it is 12:25, the clock incorrectly shows 17:75. Calculate the fraction of the day during which the clock shows the correct time.

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