
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 the circle $O: x^{2}+y^{2}=4$, two fixed points $A(a,2)$, $B(m,1)$, where $a\in\mathbb{R}$, $m > 0$. Let $P$ be any point on circle $O$, and let $\dfrac {PA}{PB}= \lambda$ (where $\lambda$ is a constant).
$(1)$ Find the value of the constant $\lambda$;
$(2)$ Draw line $l$ through the point $E(a,t)$ to intersect with the circle $C: x^{2}+y^{2}=m$ at points $M$ and $N$. If point $M$ is exactly the midpoint of segment $NE$, find the range of values for the real number $t$.

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