
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 bathtub contains \( m \) liters of water at \( t \mathrm{C}^\circ \). You remove \( v \) liters of water and replace it with \( v \) liters of water at \( d \mathrm{C}^\circ \), then repeat this process by removing another \( v \) liters of water and replacing it with \( v \) liters of water at \( d \mathrm{C}^\circ \), and so on.

a) To what temperature does the water cool down if \( m = 40001 \), \( t = 60 \mathrm{C}^\circ \), \( d = 10 \mathrm{C}^\circ \), and this process is repeated 100 times?

b) How many such water exchanges are needed for the water to cool down to \( 28 \mathrm{C}^\circ \), if \( m = 40001 \), \( t = 40 \mathrm{C}^\circ \), \( d = 15 \mathrm{C}^\circ \), and \( v = 201 \)?

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