
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) It is clear that if the side of an equilateral triangle is less than 1, then there will be broken lines of length 1 that cannot be enclosed in this triangle: an example can be simply a segment of length 1. But if the side of the equilateral triangle is greater than 1, is it possible to enclose any broken line of length 1 inside it?

b) Is it possible to enclose any convex broken line of length 1 inside an equilateral triangle with a side of length 1? (A broken line $AB$ is called convex if it, along with the segment $AB$, is the boundary of a convex polygon; see Fig. 45.)

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