
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 sheep is grazing on a vast meadow. The sheep is tied with two ropes to two posts (one rope to each post).

a) What shape will the area on the meadow be where the sheep can graze?

b) A rose is growing halfway between the posts, and the distance between the posts is 20 meters. What should be the lengths of the ropes so that the sheep cannot eat the rose?

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