
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
The simplified result of the equation $\sqrt{\left(x-4\right)^{2}+y^{2}}+\sqrt{\left(x+4\right)^{2}+y^{2}}=10$ is expressed in the form $\dfrac{x^{2}}{a}+\dfrac{y^{2}}{b}=1$, where a and b are positive real numbers. Find the values of a and b.

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