
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]


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Given vectors $$\overrightarrow {m}=(\cos \frac {x}{3}, \sqrt {3}\cos \frac {x}{3})$$, $$\overrightarrow {n}=(\sin \frac {x}{3}, \cos \frac {x}{3})$$, and $$f(x)= \overrightarrow {m}\cdot \overrightarrow {n}$$.
 (Ⅰ) Find the monotonic intervals of the function $f(x)$;
(Ⅱ) If the graph of $f(x)$ is first translated to the left by $\varphi$ ($\varphi>0$) units, and then, keeping the ordinate unchanged, the abscissa is scaled to $\frac {1}{3}$ of its original, resulting in the graph of the function $g(x)$. If $g(x)$ is an even function, find the minimum value of $\varphi$.

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