
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 string of 31 beads has one most expensive bead in the middle. Starting from one end, each subsequent bead is 3 yuan more expensive than the previous one until reaching the middle bead. Starting from the other end, each subsequent bead is 4 yuan more expensive than the previous one until reaching the middle bead. The total value of the string of beads is 2012 yuan. How much is the middle bead worth?

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