
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
In a laboratory, the speed at which sound propagates along rods made of different materials is measured. In the first experiment, it turns out that the entire path, consisting of three rods connected sequentially, is traversed by sound in $a$ seconds. The path consisting of the second and third rods is traversed by sound twice as fast as the first rod alone.

In another experiment, the second rod is replaced with a new one, and then the sequential connection of the three rods is traversed by sound in $b$ seconds. The connection of the first and second rods is twice as slow as the third rod alone.

Find the speed of sound in the new rod if its length is $l$ meters.

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