
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
In quadrilateral $ABCD$, $AB=BC=CD=2$ units, and $\angle D$ is a right angle. Angles $\angle A$, $\angle B$, and $\angle C$ are all $135^\circ$. The length of diagonal $AC$ can be expressed in simplest radical form as $a+\sqrt{b}$ units. Find the value of $a+b$.

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