
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 rods - one made of steel and the other of zinc - need to be dimensioned in such a way that their combined length at $0^{\circ}$C is $a=1 \mathrm{~m}$ and at $100^{\circ}$C is $b=1.0024 \mathrm{~m}$. How long are the two rods individually at $0^{\circ}$C if the coefficient of linear expansion for steel is $\lambda^{\prime}=0.000011$ and for zinc is $\lambda^{\prime \prime}=0.000031$?

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