
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 two vectors in the Cartesian coordinate system, $\overrightarrow{a}=(1,2)$ and $\overrightarrow{b}=(m,3m-2)$, and any vector $\overrightarrow{c}$ in the plane can be uniquely represented as $\overrightarrow{c}=\lambda \overrightarrow{a}+\mu \overrightarrow{b}$ (where $\lambda,\mu$ are real numbers), determine the range of values for $m$.

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