
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
Suppose that \( p \) is a prime number and the equation \( 2017_p + 402_p + 114_p + 230_p + 7_p = 301_p + 472_p + 503_p \) holds. How many possible values of \( p \) are there?

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