
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 $f(x)= \begin{vmatrix} \sqrt {3}\cos ^{2}x & -\sin x \\ \cos x & 1 \end{vmatrix}$.
1. Find the range of $f(x)$ when $x\in[0, \dfrac {\pi}{2}]$.
2. In triangle $ABC$, let $A$, $B$, and $C$ be the angles opposite to sides $a$, $b$, and $c$, respectively. If $f(\dfrac {A}{2})= \sqrt {3}$, $a=4$, and $b+c=5$, find the area of triangle $ABC$.

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