
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 square \(ABCD\) has sides of length 3. Set \(S\) is the set of all line segments that have length 3 and whose endpoints are on adjacent sides of the square. The midpoints of the line segments in set \(S\) enclose a region whose area, rounded to the nearest hundredth, is \(k\). Find \(100k\).

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