
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
During the Southern Song Dynasty in China, the famous mathematician Qin Jiushao independently proposed a method for calculating the area of a triangle in his work "Mathematical Treatise in Nine Sections" - the "method of three obliques for product", that is, the area $S$ of $\triangle ABC$ can be calculated as $S= \sqrt { \dfrac {1}{4}[a^{2}c^{2}-\left( \dfrac {a^{2}+c^{2}-b^{2}}{2}\right)^{2}]}$. Here, $a$, $b$, and $c$ respectively are the sides opposite to angles $A$, $B$, and $C$ in $\triangle ABC$. If $b=2$, and $\tan C= \dfrac { \sqrt {3}\sin B}{1- \sqrt {3}\cos B}$, then the maximum value of the area $S$ of $\triangle ABC$ is ______.

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