
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 sequence $\{a_n\}$ defined by the general term $a_n = 5 \left(\frac{2}{5}\right)^{2n-2} - 4 \left(\frac{2}{5}\right)^{n-1}$ where $n\in \mathbb{N}^{*}$, determine the difference between the position of the minimum term and the position of the maximum term.

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