
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 the equation in terms of $x$: $\left(|k|-3\right)x^{2}-\left(k-3\right)x+2m+1=0$ is a linear equation.<br/>$(1)$ Find the value of $k$;<br/>$(2)$ If it is known that the solutions of the equation and the equation $3x-2=4-5x+2x$ are opposite, find the value of $m$.

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