
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, $c$ respectively, and $b = \sqrt{6}$, $A = \frac{{2\pi}}{3}$. Choose one of the following conditions as known to ensure the existence and uniqueness of $\triangle ABC$:
Condition 1: $B = \frac{\pi}{4}$;
Condition 2: $a = \sqrt{3}$;
Condition 3: $a = 3$.
$(I)$ Find the value of $c$;
$(II)$ Find the area of $\triangle ABC$.

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