
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 biologist watches a chameleon. The chameleon catches flies and rests after each catch. The biologist notices that:
(i) the first fly is caught after a resting period of one minute;
(ii) the resting period before catching the \(2m^{\text{th}}\) fly is the same as the resting period before catching the \(m^{\text{th}}\) fly and one minute shorter than the resting period before catching the \((2m+1)^{\text{th}}\) fly;
(iii) when the chameleon stops resting, he catches a fly instantly.

(a) How many flies were caught by the chameleon before his first resting period of 9 minutes?
(b) After how many minutes will the chameleon catch his 98th fly?
(c) How many flies were caught by the chameleon after 1999 minutes passed?

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