
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 parametric equation of curve $C$ is given by $\begin{cases} x = 4 \cos \alpha \\ y = 4 \sin \alpha \end{cases}$ ($\alpha$ is the parameter), where $M$ is a moving point on curve $C$. If the polar coordinate equation of curve $T$ is given by $2\rho \sin \theta \rho \cos \theta = 20$,

(1) Write the Cartesian equation of curve $C$ and the rectangular coordinate equation of curve $T$.
(2) Find the maximum distance from point $M$ to curve $T$.

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