
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 an opaque bag, there are 2 red balls and 5 black balls, all identical in size and material. Balls are drawn one by one without replacement until all red balls are drawn. Calculate the expected number of draws.

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