
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 $\overrightarrow{m}=( \sqrt {3}\sin x,\cos x), \overrightarrow{n}=(\cos x,\cos x),x\in R,$ and $f(x)= \overrightarrow{m}\cdot \overrightarrow{n}$.
(I) Find the analytical expression of $f(x)$ and its monotonically increasing interval;
(II) In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $a=1$, $b+c=2$, $f(A)=1$, find the area of $\triangle ABC$.

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