
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 $2034_p + 405_p + 12_p + 212_p + 7_p = 1315_p + 541_p + 222_p$. How many possible values of $p$ are there?

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