
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 of an ellipse \(\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1\) with \(a > b > 0\) and eccentricity \(e= \frac {1}{2}\), the coordinates of the right focus are (c, 0) where c is some unknown value. Additionally, for the equation \(ax^2 + 2bx + c = 0\), find the distance from the point P(\(x_1\), \(x_2\)) to the origin.

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