
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
A circle $P$ passes through the point $M(-1,0)$ and is internally tangent to the circle $N: x^{2}+y^{2}-2x-15=0$. Let the locus of the center of circle $P$ be the curve $τ$.
(1) Find the equation of the curve $τ$;
(2) A line $l$ passing through point $M$ with a slope greater than $0$ is tangent to circle $P$ and intersects curve $τ$ at points $A$ and $B$. The midpoint of $A$ is $Q$. If the abscissa of point $Q$ is $- \frac{4}{13}$, find the radius $r$ of circle $P$.

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