
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 rewards for a certain game activity are divided into first, second, and third prizes (everyone participating in the game has a prize). The probability of winning is a geometric sequence with the first term $a$ and a common ratio of 2, and the corresponding prizes are in an arithmetic sequence with the first term of 700 yuan and a common difference of -140 yuan. What is the expected value of the prize when participating in this game activity?

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