
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 $ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite angles $A$, $B$, and $C$ respectively, with  $C= \frac{\pi}{4}$, and $2\sin^2 A - 1 = \sin^2 B$.

(1) Find the value of $\tan B$;  
(2) If $b = 1$, determine the area of the triangle $ABC$.

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