
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 line $ax+by=1$ (where $a,b$ are positive real numbers) intersects the circle $x^{2}+y^{2}=1$ at points $A$ and $B$, and the area of $\triangle AOB$ (where $O$ is the origin) is $\frac{1}{2}$, the maximum value of $a+b$ is ______.

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