
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
Let $f(x)=\sin x\cos x-\cos ^{2}\left(x+ \dfrac {\pi}{4}\right).$  
(I) Find the intervals of monotonicity for $f(x)$;  
(II) In an acute triangle $ABC$, where the sides opposite angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and given $f\left( \dfrac {A}{2}\right)=0$ and $a=1$, find the maximum area of $\triangle ABC$.

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