
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 $100$ and $999$, inclusive, is called balanced if the sum of its first digit equals the sum of its last two digits. Furthermore, the number must be even. How many such balanced integers are there?

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