
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
Spot's doghouse has a regular hexagonal base that measures two yards on each side. He is tethered to a vertex with a three-yard rope. An overhang adjacent to the doghouse creates a shaded region that Spot can also explore. This shaded region is a sector with an angle of \(90^\circ\) and radius of 1 yard located at a vertex of the hexagon two vertices away from where he is tethered. What is the area, in square yards, of the region Spot can reach, including the overhang? Express your answer in terms of \(\pi\).

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