
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
If the real numbers \(a\) and \(b\) satisfy the conditions \(\left\{\begin{array}{l}a+b-2 \geq 0 \\ b-a-1 \leq 0 \\ a \leq 1\end{array}\right.\), then the maximum value of \(\frac{a+2b}{2a+b}\) is.

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