
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
Each of a group of $50$ students is either red-haired or black-haired, and either green-eyed or gray-eyed. If there are $17$ green-eyed red-haired students, $27$ are black-haired, and $23$ are gray-eyed, then the number of gray-eyed black-haired students is:
A) 15
B) 16
C) 17
D) 18
E) 19

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