
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 the polar coordinate equation of curve $C$ is $ρ^2= \frac{36}{4\cos^2θ +9\sin^2θ}$, if $P(x,y)$ is a moving point on curve $C$, then the maximum value of $3x+4y$ is _______.

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