
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
There is an urn with 5 black, 6 white, and 7 blue balls. Someone offers to pay 3 forints to anyone who draws 2 black, 3 white, and 4 blue balls in one draw, while receiving 50 fillér for every other outcome. Is this a favorable or unfavorable bet? What would be the fair stake instead of 3 forints?

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