
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
An electronic watch displays the time as $09:15:12$ at 9:15:12 AM and 13:11:29 at 1:11:29 PM. How many times in a 24-hour day does the six digits of the time form a symmetric sequence (i.e., the time reads the same forwards and backwards, such as 01:33:10)?

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