
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, $\overrightarrow{a} =(1,3)$ and $\overrightarrow{b} =(m,2m-3)$, such that any vector $\overrightarrow{c}$ in the plane can be uniquely represented as $\overrightarrow{c} =\lambda\overrightarrow{a} +\mu\overrightarrow{b}$, determine the range of values for $m$.

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