
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 integers \(1, 2, 4, 5, 6, 9, 10, 11, 13\) are to be placed in the circles and squares below with one number in each shape.

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-005.jpg?height=76&width=672&top_left_y=846&top_left_x=691)

Each integer must be used exactly once, and the integer in each circle must be equal to the sum of the integers in the two neighbouring squares. If the integer \(x\) is placed in the leftmost square and the integer \(y\) is placed in the rightmost square, what is the largest possible value of \(x + y\)?

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