
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 polar coordinates, let the circle described by the parametric equations
$$
\begin{cases}
x= \frac { \sqrt {6}}{2}cosθ \\
y= \frac { \sqrt {6}}{2}sinθ
\end{cases}
$$
($θ$ is the parameter) have points at distance $d$ from the line described by $\rho(\sqrt{7}\cosθ - \sinθ) = \sqrt{2}$. Find the maximum value of $d$.

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