
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 $\overrightarrow{OA} = 3\overrightarrow{i} - 4\overrightarrow{j}$, $\overrightarrow{OB} = 6\overrightarrow{i} - 3\overrightarrow{j}$, and $\overrightarrow{OC} = (5-m)\overrightarrow{i} - (4+m)\overrightarrow{j}$, where $\overrightarrow{i}$ and $\overrightarrow{j}$ are the unit vectors in the positive directions of the x-axis and y-axis in a Cartesian coordinate system, respectively.
(1) If points A, B, and C can form a triangle, determine the condition that the real number \(m\) must satisfy;
(2) If \(\triangle ABC\) is a right triangle and \(\angle A\) is the right angle, find the value of \(m\).

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