
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 choir director must select a group of singers from among his $7$ tenors and $9$ basses. The selection must obey the following conditions:
- The difference between the number of tenors and basses must be a multiple of $3$.
- The total number of singers selected (tenors + basses) must be even.
- The group must have at least one singer.
Let $N$ be the number of different groups that can be selected. What is the remainder when $N$ is divided by $100$?
A) 52
B) 55
C) 56
D) 58
E) 60

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