
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 the operation $*$ defined by $a * b = a^{b^2}$ for positive integers $a$ and $b$. Determine whether the following equation holds for positive integers $a$, $b$, and $n$:
\[
(a * b)^n = a * (bn)
\]
A) True for all positive integers $a, b, n$
B) False for all positive integers $a, b, n$
C) True only when $n = 1$
D) True for all positive integers $a, b$, if $n = 1$

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