
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
For a four-digit positive integer \(ABCD\), where \(A, B, C,\) and \(D\) are digits with \(A \neq 0\) and \(D \neq 0\), we define the Reverse Digit sum (RD sum) of \(ABCD\) to be the sum of \(ABCD\) and \(DCBA\). For example, the RD sum of 1205 is \(1205 + 5021 = 6226\), while the integer 2300 does not have an RD sum.

(a) Determine the RD sum of 4281.

(b) There are positive integers \(m\) and \(n\) with the property that the RD sum of the integer \(ABCD\) is always equal to \(m \times (A + D) + n \times (B + C)\). State the value of \(m\) and the value of \(n\).

(c) Determine the number of four-digit integers whose RD sum is 3883.

(d) Determine the number of four-digit integers that are equal to the RD sum of a four-digit integer.

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