
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
In the cartesian coordinate plane xOy, M and N are two moving points on the positive semi-axis of x and the graph of y=x (x>0) respectively, and |MN| = $\sqrt{2}$, find the maximum value of |OM|^2+|ON|^2.

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