
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 line $l:y=-x+3$ and the ellipse $C:mx^{2}+ny^{2}=1(n > m > 0)$ which have exactly one common point $P(2,1)$.

(1) Find the standard equation of the ellipse $C$;

(2) If the line $l:y=-x+b$ intersects $C$ at points $A$ and $B$, and $OA⊥OB$ (where $O$ is the origin), find the value of $b$.

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