
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
Ignoring the colon, how many different palindromes are possible on a 12-hour digital clock displaying only the hours and minutes, where military time is allowed for minutes (i.e., minutes can range up to 99 instead of 59), but non-valid times are excluded? For this problem, a zero may not be inserted before a time with a single-digit hour value (i.e., 03:30 is acceptable, but 01:10 is not).

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