
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
In the below picture, \( T \) is an equilateral triangle with a side length of 5 and \( \omega \) is a circle with a radius of 2. The triangle and the circle have the same center. Let \( X \) be the area of the shaded region, and let \( Y \) be the area of the starred region. What is \( X - Y \) ?

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