
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
Max repeatedly throws a fair coin in a hurricane. For each throw, there is a  $4\%$  chance that the coin gets blown away. He records the number of heads  $H$  and the number of tails  $T$  before the coin is lost. (If the coin is blown away on a toss, no result is recorded for that toss.) What is the expected value of  $|H-T|$ ?

*Proposed by Krit Boonsiriseth.*

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