
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
What is the value of \(A^{2}+B^{3}+C^{5}\), given that:
\[ 
\begin{array}{l}
A=\sqrt[3]{16 \sqrt{2}} \\
B=\sqrt{9 \sqrt[3]{9}} \\
C=\left[(\sqrt[5]{2})^{2}\right]^{2}
\end{array}
\]

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