
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
Consider a four-digit positive integer \( M \) whose base-4 and base-7 representations are written on a blackboard. Another person, Sam, sees these numbers, treating them as base-10 integers, adds them to obtain a new integer \( T \). Determine how many choices of \( M \) result in \( T \) having its two rightmost digits, in order, the same as those of \( 3M \).
A) 24
B) 28
C) 32
D) 36
E) 40

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