
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
How many different palindromes are possible on a 12-hour digital clock displaying only the hours and minutes, when considering only even-hour values for three-digit and up to 4 possibilities (0 to 3) for the units digit of the hour in four-digit palindromes? (Zero may not be inserted before a time with a single-digit hour value, and a $\textit{palindrome}$ reads the same forward as backward.)

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