
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 segment of length $2$ is divided into four segments. Then there exists a quadrilateral with the four segments as sides if and only if each segment is:
- greater than $\frac{1}{4}$ and less than $1$.
A) Greater than $\frac{1}{8}$ and less than $\frac{3}{4}$
B) Greater than $\frac{1}{4}$ and less than $1$
C) Equal to or greater than $\frac{1}{4}$ and less than $\frac{1}{2}$
D) Greater than $0$ and less than $\frac{1}{2}$
E) Less than $1$

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