
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
Sam writes on a whiteboard the positive integers from 1 to 6 inclusive, once each. She then writes \( p \) additional fives and \( q \) sevens on the board. The mean of all the numbers on the board is then 5.3. What is the smallest possible value of \( q \)?

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