
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 a past  Mathematical Olympiad  the maximum  possible  score  on a  problem was 5. The  average score of boys  was 4,  the average  score  of girls  was 3.25, and the overall  average  score  was  3.60. Find the total number  of participants, knowing  that  it was  in the range  from  31  to 50.

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