
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 the upcoming semester, 100 math majors can take up to two out of five math electives. Suppose 22 will not take any math elective in the coming semester. Also,

- 7 will take Algebraic Number Theory and Galois Theory
- 12 will take Galois Theory and Hyperbolic Geometry
- 3 will take Hyperbolic Geometry and Cryptography
- 15 will take Cryptography and Topology
- 8 will take Topology and Algebraic Number Theory

Everyone else will take only one math elective. Furthermore, 16 will take either Algebraic Number Theory or Cryptography, but not both. How many math majors will take exactly one of Galois Theory, Hyperbolic Geometry, or Topology?

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