
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
There is a sports competition with \( M \) events. Athletes \( A, B, \) and \( C \) participate. In each event, the first, second, and third places earn \( p_{1}, p_{2}, p_{3} \) points, respectively, where \( p_{1}, p_{2}, p_{3} \) are positive integers, and \( p_{1} > p_{2} > p_{3} \).

- Athlete \( A \) ends up with 22 points.
- Athletes \( B \) and \( C \) both end up with 9 points.
- Athlete \( B \) took first place in the 100-meter race.

Determine the value of \( M \) and identify who placed second in the high jump event.

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