
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 faulty $12$-hour digital clock shows the time such that whenever it should show a '2', it mistakenly displays a '5'. For instance, when the correct time is 2:25 PM, the clock incorrectly shows 5:55 PM. Calculate the fraction of the day during which the clock displays the correct time.

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