
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 real numbers \( x, y \) and \( z \) satisfy the condition \( x + y + z = 3 \), find the maximum value of \( f(x, y, z) = \sqrt{2x + 13} + \sqrt[3]{3y + 5} + \sqrt[4]{8z + 12} \).

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