
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 the function $f(x)=-\sin^2x-\sqrt{3}\sin x\cos x+\frac{1}{2}$.

(Ⅰ) Find the intervals of monotonic decrease for the function $f(x)$;

(Ⅱ) In an acute triangle $\Delta ABC$, with the opposite sides of angles $A$, $B$, $C$ being $a$, $b$, $c$ respectively, it is known that $f(A)=-1$, $a=2$, and $b\sin C=a\sin A$. Find the area of $\Delta ABC$.

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