
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
Equilateral triangle \(ABC\) with side length 1 is drawn. A square is drawn such that its vertex at \(A\) is opposite to its vertex at the midpoint of \(BC\). Find the area enclosed within the intersection of the insides of the triangle and square. Hint: \(\sin 75^\circ = \frac{\sqrt{2}(\sqrt{3}+1)}{4}\).

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