
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
On each day of their tour of the West Indies, Sourav and Srinath have either an apple or an orange for breakfast. Sourav has oranges for the first  $m$  days, apples for the next  $m$  days, followed by oranges for the next  $m$  days, and so on. Srinath has oranges for the first  $n$  days, apples for the next  $n$  days, followed by oranges for the next  $n$  days, and so on.
If  $\gcd(m,n)=1$ , and if the tour lasted for  $mn$  days, on how many days did they eat the same kind of fruit?

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