
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
Two homogeneous rods with equal cross-sectional areas, different densities, and different coefficients of expansion are welded together in such a way that the system's center of gravity remains unchanged despite thermal expansion. How do the lengths of the rods relate to each other?

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