
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 class of 35 students can be divided into two groups: "Cubeheads" and "Tall people." The Tall people claim they are taller than the Cubeheads, who, in turn, believe they are better at math. One Cubehead once asked a Tall person: "What do you mean that you are taller than us? Do you mean that:

1. Every Tall person is taller than every Cubehead?
2. The tallest Tall person is taller than the tallest Cubehead?
3. Every Tall person is taller than at least one Cubehead?
4. Every Cubehead is shorter than at least one Tall person?
5. The shortest Cubehead is shorter than the shortest Tall person?"

Upon hearing these questions, the Tall person visibly shrank . . . The task is to determine the relationships among these statements, i.e., for any two statements, decide whether one implies the other.

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