
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
Given that point $(m, n)$ lies on the curve $\begin{cases} x= \sqrt {6}\cos\alpha \\ y= \sqrt {6}\sin\alpha \end{cases}$ (where $\alpha$ is a parameter), and point $(x, y)$ lies on the curve $\begin{cases} x= \sqrt {24}\cos\beta \\ y= \sqrt {24}\sin\beta \end{cases}$ (where $\beta$ is a parameter), find the maximum value of $mx+ny$.

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