
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 polar coordinate system, let the point on the circle $ \begin{cases}x= \frac{ \sqrt{6}}{2}\cos \theta \\ y= \frac{ \sqrt{6}}{2}\sin \theta \end{cases} (\theta \text{ is a parameter}) $ have a distance $d$ from the line $ρ( \sqrt{7}\cos θ-\sin θ)= \sqrt{2}$. Find the maximum value of $d$.

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