
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
The sides opposite to the internal angles of $\triangle ABC$ are $a$, $b$, and $c$, respectively, satisfying $a^{2}+2b^{2}=c^{2}$.
$(1)$ If $A= \frac {\pi}{3},b=1$, find the area of $\triangle ABC$;
$(2)$ Find $\frac {\tan C}{\tan A}$.

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