
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 12-hour digital clock shows time inaccurately not just for '1', which it displays as '9', but now also for every '2', which it displays as '5'. Consequently, when the clock should show 2:21 PM, it incorrectly shows 5:59 PM instead. Calculate the fraction of the day when the clock will show the correct time.

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