
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 discrete random variable $\xi$ which can take the values of $1$, $2$, and $3$, where $P(\xi=k)=ak+b\ (k=1,2,3)$, if the expected value of $\xi$ is $E\xi=\frac{7}{3}$, then find the value of $a+b$.

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