
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 functions $f(x)=e^{x}-e^{-x}$ and $g(x)=e^{x}+e^{-x}$,

(1) Find the value of $[f(x)]^{2}-[g(x)]^{2}$;
(2) If $f(x)⋅f(y)=4$ and $g(x)⋅g(y)=8$, find the value of $\frac {g(x+y)}{g(x-y)}$.

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