
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.  $y = c$  intersects the curve  $y = 2x - 3x^3$  at  $P$  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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