
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 angle bisector of the acute angle formed at the origin by the graphs of the lines $y = 2x$ and $y = 4x$ has equation $y = mx.$ Determine $m.$
- **A)** $\frac{\sqrt{21}}{7}$
- **B)** $\frac{6 - \sqrt{21}}{7}$
- **C)** $\frac{\sqrt{21} - 6}{7}$
- **D)** $\frac{6 + \sqrt{21}}{7}$
- **E)** $\frac{\sqrt{21} + 6}{7}$

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