
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

The Magic Kingdom Treasury wants to replace all old banknotes with new ones. There are a total of 3,628,800 old banknotes in the treasury. The machine, which prints new banknotes, unfortunately, requires major repairs and each day it can print fewer banknotes: on the first day, it can print only half of the banknotes that need replacement; on the second day, only a third of the remaining old banknotes in the treasury; on the third day, only a quarter of the remaining old banknotes, and so on. Each operation of the machine, regardless of its condition, costs the treasury 90,000 currency units (c.u.), and the major repair will cost 800,000 c.u. After the major repair, the machine can print no more than one million banknotes per day. The budget allocated for updating banknotes from the treasury is no more than 1 million c.u.

(a) In how many days will $80 \%$ of the old banknotes be replaced?

(b) Will the kingdom be able to replace all the old banknotes in the treasury?

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