
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 \(w\) and \(z\) are complex numbers such that \(|w+z|=1\) and \(\left|w^{2}+z^{2}\right|=14\), find the smallest possible value of \(\left|w^{3}+z^{3}\right|\). Here, \(|\cdot|\) denotes the absolute value of a complex number, given by \(|a+bi|=\sqrt{a^{2}+b^{2}}\) whenever \(a\) and \(b\) are real numbers.

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