
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
Alena, Bára, Čeněk, and David bought a tandem bicycle for two. They always go for a ride in pairs. Each person has ridden with every other person at least once, and no one else has ridden the tandem. Alena has gone for a ride eleven times, Bára twenty times, and Čeněk only four times.

Determine the minimum and maximum number of times David could have gone for a ride.

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