
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 an ellipse $(C)$: $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a > b > 0)$ passing through point $P(-1, -1)$, $c$ is the semi-focal distance of the ellipse, and $c = \sqrt{2}b$. Two perpendicular lines $l_{1}$ and $l_{2}$ are drawn through point $P$, intersecting ellipse $(C)$ at two other points $M$ and $N$.

1. Find the equation of ellipse $(C)$;
2. If the slope of line $l_{1}$ is $(-1)$, find the area of $\triangle PMN$.

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