
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 a circle C: $x^2+y^2+x-6y+m=0$ and a line $l: x+2y-3=0$.

(1) When $m= \frac {5}{4}$, determine the positional relationship between circle C and line $l$;  
(2) If line $l$ and circle C have no common points, find the range of values for $m$;  
(3) If line $l$ intersects circle C at points P and Q, and O is the origin, and the circle with diameter PQ passes through point O, find the value of the real number $m$.

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