
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 a certain tech innovation competition, there are first, second, and third prizes (every participant will receive a prize), and the corresponding probabilities of winning these prizes form an geometric sequence with the first term $a$ and common ratio $2$. The respective prize money for these prizes are $7000, $5600, and $4200. The expected prize money for participating in this competition is _______ dollars.

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