
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 a triangle $ABC$ with angles $A$, $B$, $C$ and opposite sides $a$, $b$, $c$ respectively, and it satisfies $\sin^2B + \sin^2C - \sin^2A = \sin B \sin C$  
$(1)$ Find the measure of angle $A$;  
$(2)$ Given the function $f(x) = \sin (\omega x + A)$, where $\omega > 0$ and the smallest positive period is $\pi$, find the intervals where $f(x)$ is decreasing.

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