
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
An event has arranged $4$ programs, and each audience member has $6$ identical tickets. After the event, all tickets will be given to their favorite program. One audience member's favorite program is program $A$, and they plan to give at least $3$ tickets to that program. The remaining tickets will be randomly distributed among the other programs, with program $A$ receiving the most votes. Calculate the number of ways in which the $4$ programs can receive the audience member's tickets.

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