
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]


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Given a hyperbola with its center at the origin, and its foci $F_{1}$ and $F_{2}$ on the coordinate axes. The equations of the asymptotes are $y=±x$, and the hyperbola passes through the point $P(4,- \sqrt {10})$.  
$(1)$ Find the equation of the hyperbola;  
$(2)$ If point $M(x_{1},y_{1})$ is on the hyperbola, find the range of $\overrightarrow{MF_{1}}\cdot \overrightarrow{MF_{2}}$.

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