
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 that the random variable $\xi$ follows the normal distribution $N(2,9)$, if $P(\xi>3)=a$, $P(1<\xi\leq3)=b$, then the range of the function $$f(a)= \frac {a^{2}+a-1}{a+1}$$ is \_\_\_\_\_\_.

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