
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 vectors $\overrightarrow{m}=(1,\cos x)$ and $\overrightarrow{n}=(t, \sqrt {3}\sin x-\cos x)$, the graph of the function $f(x)= \overrightarrow{m} \cdot \overrightarrow{n}$ $(t\in R)$ passes through point $M( \frac {\pi}{12},0)$.
(I) Find the value of $t$, the smallest positive period, and the interval on which the function is increasing;
(II) In $\triangle ABC$, let the sides opposite angles $A$, $B$, and $C$ be $a$, $b$, and $c$, respectively. If $a= \frac {\cos B+b\cos C}{2\cos B}$, find the range of $f(A)$.

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