
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 that point $P$ is any point on the circle $x^{2}+y^{2}=25$, a vertical line is drawn from $P$ to the $x$-axis, with the foot of the perpendicular being $H$. If $ \overrightarrow{MH}= \frac {3}{5} \overrightarrow{PH}$, and the locus of $M$ is curve $E$.
  
(1) Find the equation of $h(x)=f(x)-g(x)$;
  
(2) Suppose two chords $MN$ and $PQ$ pass through the left focus of curve $E$, with the slopes of the lines containing $MN$ and $PQ$ being $k_{1}$ and $k_{2}$ respectively. Determine whether $ \frac {1}{|MN|}+ \frac {1}{|PQ|}$ is a constant value. If it is, find this value; if not, explain why.

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