
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
Let $\triangle ABC$ have sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ respectively. Given that $\frac{{{b^2}+{c^2}-{a^2}}}{{\cos A}}=2$. Find:<br/>
$(1)$ $bc$;<br/>
$(2)$ If $\frac{{a\cos B-b\cos A}}{{a\cos B+b\cos A}}-\frac{b}{c}=1$, find the area of $\triangle ABC$.

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