
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
Dima saw a strange clock in a museum (see the diagram). Unlike regular clocks, this one has no numbers on its dial, and it is impossible to tell the top of the clock; moreover, the second, minute, and hour hands are all the same length. What time does the clock show?

(Note: Hands A and B on the drawing point exactly to the hour markers, while hand C is slightly off from an hour marker.)

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