
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 graph of the function $y=\log_a(x+3)-1$ (where $a>0$ and $a\neq1$) always passes through a fixed point A, and point A also lies on the graph of the function $f(x)=3^x+b$, find the value of $f(\log_3 2)$.

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