
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 $f(x)=\frac{1}{2}-\cos^2x+\sqrt{3}\sin x\cos x$,
1. Find the interval where $f(x)$ is monotonically decreasing.
2. In triangle $ABC$, if the sides opposite angles $A$, $B$, and $C$ denoted by $a$, $b$, and $c$ satisfy the condition $b^2+c^2-a^2>bc$, find the range of $f(A)$.

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