
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 a triangle $\vartriangle ABC$, where the sides opposite to the angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively.

(I) If $b=\sqrt{3}$, $A=45^{0}$, $C=75^{0}$, find the value of $a$.

(II) If ${b}^{2}={a}^{2}+{c}^{2}+\sqrt{2}ac$, find the value of angle $B$.

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