
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
For how many ordered pairs of positive integers  $(a,b)$  with  $a,b<1000$  is it true that  $a$  times  $b$  is equal to  $b^2$  divided by  $a$ ? For example,  $3$  times  $9$  is equal to  $9^2$  divided by  $3$ .

*Ray Li*

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