
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 game event, the rewards are divided into first, second, and third prizes, and the corresponding probabilities to win are in a geometric sequence with the first term $a_1$ and a common ratio of 2. The corresponding prize money is in an arithmetic sequence with the first term 700 yuan and a common difference of -140 yuan. The expected prize money obtained from participating in the game is ____ yuan.

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