
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
The point $A(5,1)$ is symmetric about the $x$-axis at point $B(x_{1},y_{1})$, and symmetric about the origin at point $C(x_{2},y_{2})$.
(1) Find the equation of the line passing through the midpoints of sides $BA$ and $BC$ in $\triangle ABC$;
(2) Find the area of $\triangle ABC$.

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