
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 sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. It is given that $a \sin A + c \sin C - \sqrt{2} a \sin C = b \sin B$.

$(1)$ Find $B$;

$(2)$ If $A = 75^{\circ}$ and $b = 2$, find $a$ and $c$.

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