
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 $f(x)=4acosxsin(x- \frac {π}{6})$, and $f( \frac {π}{3})=1$.
(Ⅰ) Find the value of $a$ and the smallest positive period of $f(x)$;
(Ⅱ) If $f(x)$ is monotonically increasing in the interval $[0, m]$, find the maximum value of $m$.

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