
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
Fill in the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 into the squares below such that the sum of the two five-digit numbers equals 99,999. How many different addition equations (considering $a + b$ and $b + a$ as the same equation) are there?
$\square \square \square \square \square + \square \square \square \square \square = 99999$

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