
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 bag, there are 5 balls of the same size, including 2 white balls, 2 black balls, and 1 red ball. Now, one ball is drawn from the bag each time without replacement until two balls of different colors are drawn, at which point the process stops. Let X represent the number of draws needed to stop the process. Calculate the mathematical expectation E(X) of the random variable X.

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