
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 vectors $\overrightarrow {OA} = (2, -1)$, $\overrightarrow {OB} = (3, 2)$, and $\overrightarrow {OC} = (m, 2m+1)$. If points A, B, and C can form a triangle,
(1) find the condition that the real number $m$ must satisfy;
(2) if $\triangle ABC$ is a right-angled triangle, find the value of $m$.

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