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

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