
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
Let ellipse $C$ be given by the equation: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1 (a>b>0).$$ Points $M$ and $N$ are at the two ends of the major axis. If there exists a point $H$ on the ellipse such that the product of the slopes of lines $MH$ and $NH$ falls within the interval $(- \frac {1}{2}, 0)$, find the range of values for the eccentricity $e$ of the ellipse.

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