
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
Let \( a \) and \( b \) be complex numbers satisfying the two equations
\[ 
\begin{array}{c}
a^{3}-3 a b^{2}=36 \\
b^{3}-3 b a^{2}=28i .
\end{array}
\]

Let \( M \) be the maximum possible magnitude of \( a \). Find all \( a \) such that \( |a|=M \).

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