
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, \(BC = CD = 3\) units, and \(\angle E\) is a right angle. Assume that \(m \angle B = 120^\circ\), \(m \angle C = 90^\circ\), and \(m \angle D = 135^\circ\). The length of segment \(AE\) can be expressed in simplest radical form as \(a + 3\sqrt{b}\) units. What is the value of \(a+b\)?

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