
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
Consider that \( p \) is a prime number and the equation \( 2006_p + 404_p + 215_p + 222_p + 9_p = 433_p + 572_p + 321_p \). How many possible values of \( p \) are there?

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