
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 math teacher, while teaching reasoning and proof, uses Go pieces as teaching aids. He has 4 white Go pieces and 3 black Go pieces in his pocket. Each time he draws one piece without putting it back, he lets the students guess the color of the next piece drawn.
(1) Calculate the probability that the first two pieces drawn by the teacher are of the same color;
(2) If the number of white Go pieces drawn in the first four draws is denoted by $\eta$, calculate $E\eta$.

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