
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
Find the trajectory of a point M $(x, y)$ given that the ratio of its distance from the fixed point F $(1, 0)$ to its distance from the line $l: x = 2$ is $\frac{\sqrt{2}}{2}$.
(Ⅰ) Determine the trajectory of point M.
(Ⅱ) Is there a maximum distance from point M to the line $\frac{x}{\sqrt{2}} + y = 1$? If so, what is that maximum distance?

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