
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 sum of the squares of three positive numbers is  $160$ . One of the numbers is equal to the sum of the other two. The difference between the smaller two numbers is  $4.$  What is the difference between the cubes of the smaller two numbers?

*Author: Ray Li*

<details><summary>Clarification</summary>The problem should ask for the positive difference.</details>

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