
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
The expression \(\frac{a^{-2}}{a^{5}} \times \frac{4 a}{(2^{-1} a)^{-3}}\), where \(a \neq 0\), is equal to:
(a) \(\frac{a^{3}}{2}\);
(b) \(\frac{2}{a^{3}}\);
(c) \(\frac{1}{2 a^{3}}\);
(d) \(\frac{a^{5}}{2}\);
(e) \(\frac{2}{a^{5}}\).

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