
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
Peter, Paul, and David joined a table tennis tournament. On the first day, two of them were randomly chosen to play a game against each other. On each subsequent day, the loser of the game on the previous day would take a rest, and the other two persons would play a game against each other. After a certain number of days, it was found that Peter had won 22 games, Paul had won 20 games, and David had won 32 games. What was the total number of games that Peter had played?

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