
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 hyperbola that passes through point $P(-3 \sqrt {2},4)$, its asymptote lines are represented by the equations $y=± \frac {4}{3}x$.
(1) Find the standard equation of the hyperbola;
(2) Let $F\_{1}$ and $F\_{2}$ be the left and right foci of the hyperbola, respectively, and point $P$ is on the hyperbola with $|PF\_{1}|⋅|PF\_{2}|=41$, find the cosine value of $∠F\_{1}PF\_{2}$.

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