
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 \(ABCD\), it is given that \(\angle ABC = 135^\circ\), \(\angle BCD = 120^\circ\), \(AB = \sqrt{6}\), \(BC \approx 5 - \sqrt{3}\), and \(CD = 6\). Find the length of \(AD\).

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