
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 $C: \frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1(a>0,b>0)$ with eccentricity $e=2$, the distance from one focus of the hyperbola $C$ to an asymptote is $\sqrt {3}$  
(1) Find the equation of the hyperbola $C$  
(2) A line $l$ passing through point $M(5,0)$ intersects the hyperbola $C$ at points $A$ and $B$, and intersects the y-axis at point $N$. When $\overrightarrow {NM}=\lambda \overrightarrow {AM}=\mu \overrightarrow {BM}$, and $( \frac {1}{\lambda })^{2}+( \frac {1}{\mu })^{2}=( \frac {7}{5})^{2}$, find the equation of line $l$.

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