
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 real numbers \( x \) and \( y \) that satisfy \( x^{2} + y^{2} \leq 5 \), find the maximum and minimum values of the function \( f(x, y) = 3|x+y| + |4y+9| + |7y-3x-18| \).

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