
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 $f(x)=( \sqrt {3}\tan x+1)\cos ^{2}x.$  
$(1)$ If $\alpha\in\left( \frac {\pi}{2},\pi\right)$, and $\cos \alpha=- \frac { \sqrt {5}}{5}$, find the value of $f(\alpha)$;  
$(2)$ Discuss the monotonicity of the function $f(x)$ in the range $x\geqslant \frac {\pi}{4}$, and $x\leqslant \frac {3\pi}{4}$.

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