
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
Given the function $f(x)=\sin ^{2}x+ \sqrt {3}\tan θ\cdot\cos x+ \frac { \sqrt {3}}{8}\tan θ- \frac {3}{2}$, where $x\in\left[0, \frac {π}{2}\right]$, $θ\in\left[0, \frac {π}{3}\right]$
(1) When $θ= \frac {π}{3}$, find the maximum value of $f(x)$ and the corresponding value of $x$;
(2) Does there exist a real number $θ$ such that the maximum value of the function $f(x)$ is $- \frac {1}{8}$? If it exists, find the corresponding $θ$ value; if not, explain the reason.

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