
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
A certain city plans to renovate a road in the urban area of length $S$ meters in order to pass the evaluation for the "National Civilized City" title. Two construction teams, Team A and Team B, are arranged to carry out the construction work.

(1) It is known that Team A takes the same amount of time to renovate a road of $360$ meters as Team B takes to renovate a road of $300$ meters. If Team A renovates $30$ meters more than Team B each day, find the length of road renovated by Team A and Team B each day.

(2) If Team A can renovate $a$ meters of road each day and Team B can renovate $b$ meters of road each day (where $a\neq b$), there are two construction plans:

Plan 1: Team A renovates the first $\dfrac{1}{2}S$ meters of the road, and Team B renovates the last $\dfrac{1}{2}S$ meters.

Plan 2: Team A renovates the road for the first half of the total time, and Team B renovates the road for the second half of the total time.

Based on the above descriptions, determine which renovation plan takes less time and explain the reason.

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