
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 that in triangle $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $B = \frac{π}{4}$. <br/>$(1)$ Please choose one of the following conditions as the given condition and find the value of $\sin A$; <br/>① $b = \sqrt{5}$, $c = \sqrt{2}$; ② $a = 3$, $c = \sqrt{2}$. <br/>$(2)$ If $b = \sqrt{5}$ and $a + c = 3$, find the area of $\triangle ABC$.

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