
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
Bernardo selects a four-digit integer \(N\) and writes its base-7 and base-8 representations on a whiteboard. Later, Rebecca sums these numbers thinking of them as base-10 integers to get \(T\). If the sum \(T\) satisfies \(T \equiv 4N \mod 1000\) then for how many values of \(N\) does this condition hold true?
A) 22
B) 44
C) 55
D) 66
E) 77

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