
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
At the beginning of each hour from  $1$  o’clock AM to  $12$  NOON and from  $1$  o’clock PM to  $12$  MIDNIGHT a coo-coo clock’s coo-coo bird coo-coos the number of times equal to the number of the hour. In addition, the coo-coo clock’s coo-coo bird coo-coos a single time at  $30$  minutes past each hour. How many times does the coo-coo bird coo-coo from  $12:42$  PM on Monday until  $3:42$  AM on Wednesday?

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