
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 that the graph of $$f(x)=-\cos^{2} \frac {ω}{2}x+ \frac { \sqrt {3}}{2}\sinωx$$ has a distance of $$\frac {π}{2}(ω＞0)$$ between two adjacent axes of symmetry.  
(Ⅰ) Find the intervals where $f(x)$ is strictly decreasing;  
(Ⅱ) In triangle ABC, a, b, and c are the sides opposite to angles A, B, and C, respectively. If $$f(A)= \frac {1}{2}$$, $c=3$, and the area of triangle ABC is $$3 \sqrt {3}$$, find the value of a.

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