
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 mutually perpendicular axes $O x$ and $O y$, and a point $A(a, a)$ where $a > 0$. It is required to find the coordinates of a point $M$ on the $O x$ axis and a point $P$ on the $O y$ axis such that the triangle $A M P$ is equilateral.

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