
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 a non-zero natural number, if it is even, divide it by 2; if it is odd, multiply it by 3 and add 1. This transformation yields a new natural number. Repeating this process raises the question: Does every natural number eventually transform to 1? This is known as the "Collatz Conjecture" in mathematics. If a number transforms to 1 through this process, the number of transformations needed the first time it reaches 1 is called its path length. What is the sum of all natural numbers with a path length of 10 in the context of the "Collatz Conjecture"?

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