
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
There is a square-shaped park with side length $a$, and in the center of the park, there is a circular flowerbed with diameter $d$. Around the park and along the edge of the flowerbed, there is a continuous path. There are also straight paths leading from the corners and midpoints of the sides of the square towards the center up to the flowerbed. What is the shortest path from one corner of the park to the opposite corner?

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