
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  $(a,b)$  is an ordered pair of integers such that the three numbers  $a$ ,  $b$ , and  $ab$  form an arithmetic progression, in that order. Find the sum of all possible values of  $a$ .

*Proposed by Nathan Xiong*

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