
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
In $\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. Given vectors $\overrightarrow {m}=(2a+c, b)$ and $\overrightarrow {n}=(\cos B, \cos C)$ such that $\overrightarrow {m} \cdot \overrightarrow {n} = 0$.
(I) Determine the measure of angle $B$.
(II) If the angle bisector $BD$ of $\angle ABC$ intersects $AC$ at $D$, and $BD=1$, let $BC=x$, $BA=y$. Determine the functional relationship between $y$ and $x$, and investigate the value of $x$ that minimizes the area of $\triangle ABC$.

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