
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 parabola $C: y^{2}=2px(p > 0)$, the distance from point $P(2,t)$ in the first quadrant to the focus $F$ is $\frac {5}{2}$.  
$(1)$ If $M(- \frac {1}{2},0)$, and the line $l_{1}$ through points $M$ and $P$ intersects the parabola at another point $Q$, find the value of $\frac {|QF|}{|PF|}$;  
$(2)$ If the line $l_{2}$ intersects the parabola $C$ at points $A$ and $B$, and intersects the circle $M: (x-a)^{2}+y^{2}=1$ at points $D$ and $E$, with $O$ being the origin and $OA \perp OB$, is there a real number $a$ such that the length of $|DE|$ is constant? If so, find the value of $a$; if not, explain why.

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