
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 $\triangle ABC$, $BC = \sqrt{5}$, $AC = 3$, and $\sin C = 2\sin A$.
(1) Find the value of $AB$;
(2) Find $\sin\left(2A - \frac{\pi}{4}\right)$.

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