
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
The complex numbers $z_{1}=3+4i$, $z_{2}=0$, $z_{3}=c+(2c-6)i$ correspond to points $A$, $B$, $C$ in the complex plane, respectively. If $\angle BAC$ is an obtuse angle, then the range of the real number $c$ is ______.

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