
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
An integer between $2000$ and $9999$, inclusive, is called balanced if the difference between the sum of its two leftmost digits and the sum of its two rightmost digits equals 2. How many balanced integers are there?

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