
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
A number between $100$ and $9999$, inclusive, is called "digitally balanced" if the sum of its leftmost digit(s) and its middle digit equals the sum of its remaining digits. For three-digit numbers, if the number is $abc$, it is balanced if $a + b = c$. For four-digit numbers, if the number is $abcd$, it is balanced if $a + b = c + d$. How many digitally balanced numbers are there between $100$ and $9999$?

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