
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
Given the distribution table of the random variable $X$, where $P(X=0)=\frac{8}{27}$, $P(X=1)=\frac{4}{9}$, $P(X=3)=\frac{1}{27}$, and $P(X=2)=m$, calculate the mean $E(X)$.

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