
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 $\triangle ABC$, the sides $a$, $b$, and $c$ correspond to angles $A$, $B$, and $C$ respectively. Given that $a= \sqrt{5} $, $b=3$, and $\sin C=2\sin A$.

(1) Find the value of $c$;

(2) Find the value of $\sin (2A- \frac{π}{4} )$.

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