
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  $a$  and  $ b$  are distinct positive integers satisfying  $20a + 17b = p$  and   $17a + 20b = q$  for certain primes  $p$  and  $ q$ . Determine the minimum value of  $p + q$ .

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