
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
(1) A train is 400 meters long. It takes 10 minutes for the train to pass through a tunnel (from the moment the front of the train enters the tunnel until the rear of the train exits the tunnel). If the speed increases by 0.1 kilometers per minute, it only takes 9 minutes. Find the length of the tunnel.  
(2) Two people, A and B, went to a grain store to buy rice on two occasions, with the price of rice being $a$ yuan per jin (a unit of weight) on the first occasion and $b$ yuan per jin on the second occasion ($a \neq b$). Person A buys 100 jin of rice each time, while person B buys 100 yuan worth of rice each time. Who has a lower average price for the rice bought over the two occasions? Explain your reasoning.

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