
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
All the prime numbers are written in order,  $p_1 = 2, p_2 = 3, p_3 = 5, ...$ Find all pairs of positive integers  $a$  and  $b$  with  $a - b \geq 2$ , such that  $p_a - p_b$  divides  $2(a-b)$ .

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