
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 the parabola be $x^{2}=2py$ $(P > 0)$, and let $M$ be any point on the line $y=-2p$. A tangent line is drawn from $M$ to the parabola, and the points of tangency are $A$ and $B$. The $x$-coordinates of $A$, $B$, and $M$ are $X_{A}$, $X_{B}$, and $X_{M}$, respectively. Determine the relationship between $X_{A}$, $X_{B}$, and $X_{M}$.

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