
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
Let \(\mathrm{AB}\) be the major axis of the ellipse \(\frac{x^{2}}{16}+\frac{y^{2}}{6}=1\). The chord \(\mathrm{PQ}\) of this ellipse passes through point \(\mathrm{C}(2,0)\) but does not pass through the origin. Line \(\mathrm{AP}\) intersects \(\mathrm{QB}\) at point \(\mathrm{M}\), and \(\mathrm{PB}\) intersects \(\mathrm{AQ}\) at point \(\mathrm{N}\). Find the equation of the line \(\mathrm{MN}\).

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