
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
Several teams participated in a mental math competition. Each team received a natural number and had to find the largest and smallest odd divisors greater than 1 of that number. All teams solved their tasks correctly. Upon reviewing the results, it turned out that the original number given to any team could be represented as $15M + 11m$, where $M$ is the largest odd divisor and $m$ is the smallest odd divisor greater than 1. How many teams participated in the competition and for which numbers did the teams find the divisors?

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