
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
A day can be evenly divided into 36,000 periods of 2.4 seconds; 18,000 periods of each 4.8 seconds; or in many other ways. In total, how many ways are there to divide a day into $n$ periods of $m$ seconds, where $n$ and $m$ are positive integers and the total number of seconds in a day is 86,400?

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