
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 pentagon $ABCDE$, $BC=CD=DE=3$ units, $\angle B = 135^\circ$, and $\angle C = \angle D = 120^\circ$, $\angle A = 90^\circ$. $AE$ is a diagonal. Find the length of $AE$, which can be expressed in simplest radical form as $a + 3\sqrt{b}$ units. What is $a+b$?

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