
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 \(O\) be the origin. The line \(y = c\) intersects the curve \(y = 2x - 3x^3\) at points \(P\) and \(Q\) in the first quadrant and cuts the y-axis at \(R\). Find \(c\) so that the region \(OPR\) bounded by the y-axis, the line \(y = c\), and the curve has the same area as the region between \(P\) and \(Q\) under the curve and above the line \(y = c\).

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