
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 a triangle $\triangle ABC$ with angles $A$, $B$, $C$ and corresponding sides $a$, $b$, $c$. If the area of the triangle is given by $S=a^2-(b-c)^2$,

(I) Find the value of $\tan\frac{A}{2}$;

(II) Find the value of $\sin A + \cos A$;

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