
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 two positive real numbers $a$ and $b$, and a point $(x, y)$ satisfying $0 < x < a$ and $0 < y < b$, find the coordinates of the point $(x, y)$ which minimizes the expression $\sqrt{x^2 + y^2} + \sqrt{x^2 + (b-y)^2} + \sqrt{(a-x)^2 + y^2} + \sqrt{(a-x)^2 + (b-y)^2}$.

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