
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 triangle $ \triangle ABC $, the sides opposite to the internal angles A, B, and C are denoted as $ a $, $ b $, and $ c $, respectively, with $ b = \sqrt {3} $. Given that $ \sqrt {3} \sin C = (\sin A + \sqrt {3} \cos A) \sin B $, the maximum value of the height from vertex A to side $ AC $ is \_\_\_\_\_\_.

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