
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 \( a, b, c, x \) be real numbers with \( (a+b)(b+c)(c+a) \neq 0 \) that satisfy
\[
\frac{a^2}{a+b} = \frac{a^2}{a+c} + 20, \quad \frac{b^2}{b+c} = \frac{b^2}{b+a} + 14, \quad \text{and} \quad \frac{c^2}{c+a} = \frac{c^2}{c+b} + x
\]
Compute \( x \).

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