
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 order to treat a certain epidemic disease, a doctor prescribed an antibiotic to a patient, with instructions to take one tablet at 8 AM every day. It is known that each tablet contains 128 milligrams of medication, and his kidneys can filter out 50% of this medication from his body each day. The questions are:  
(1) After how many days will the first tablet taken by the patient have less than 1 milligram remaining in his body?  
(2) If the body requires a minimum of 25 milligrams of the medication to resist the disease, and the patient can resist the disease for the first 6 days after starting the medication, for how many days must the patient continuously take the medication at a minimum?

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