
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
How many ordered pairs of nonnegative integers  $\left(a,b\right)$  are there with  $a+b=999$  such that each of  $a$  and  $b$  consists of at most two different digits? (These distinct digits need not be the same digits in both  $a$  and  $b$ . For example, we might have  $a=622$  and  $b=377$ .)

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