
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

It is very boring to look at a black-and-white clock face, so Clive painted the number 12 red exactly at noon and decided to paint the current hour red every 57 hours.

a) How many numbers on the clock face will be painted?

b) How many numbers will be red if Clive paints them every 2005th hour?

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