
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
The intersection of line $l_1: x + y - 2\sqrt{2} = 0$ and line $l_2: \begin{cases} x= \frac{\sqrt{2}}{2}t \\ y= \frac{\sqrt{2}}{2}t \end{cases}$ (where $t$ is a parameter) to the origin $O$ has a distance of $d$. Calculate the distance $d$.

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