
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 system $(xOy)$, $P$ is a point on the line $2x+2y-1=0$, and $Q$ is a point on the ray $OP$ such that $|OP| \cdot |OQ| = 1$.
(I) Find the locus of point $Q$;
(II) Let point $M(x, y)$ be any point on the locus found in (I), find the maximum value of $x + 7y$.

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