
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
Given an acute triangle $\triangle ABC$ with internal angles $A$, $B$, and $C$, vector $\mathbf{p} = (\cos A + \sin A, 2 - 2\sin A)$, and vector $\mathbf{q} = (\cos A - \sin A, 1 + \sin A)$, and $\mathbf{p} \perp \mathbf{q}$.

(1) Find angle $A$;  
(2) Let $AC = 2$, and $\sin^2 A + \sin^2 B = \sin^2 C$, find the area of $\triangle ABC$.

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