
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. If $1+ \dfrac {\tan A}{\tan B}= \dfrac {2c}{b}$,  
$(1)$ find the size of angle $A$;  
$(2)$ if the function $f(x)=2\sin ^{2}(x+ \dfrac {\pi}{4})- \sqrt {3}\cos 2x$, $x\in\left[ \dfrac {\pi}{4}, \dfrac {\pi}{2}\right]$, reaches its maximum value $a$ at $x=B$, find the area of $\triangle ABC$.

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