
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 S that passes through points A(7, 8) and B(8, 7), with its center S on the line $2x-y-4=0$.
(1) Find the equation of circle S.
(2) If the line $x+y-m=0$ intersects circle S at points C and D, and $\angle COD$ is an obtuse angle (O is the origin), find the range of the real number $m$.

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