
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 $$\overrightarrow {m}=(\sin(x- \frac {\pi}{6}), 1), \overrightarrow {n}=(\cos x, 1)$$,  
(1) If $$\overrightarrow {m} \parallel \overrightarrow {n}$$, find the value of $\tan x$;  
(2) If the function $$f(x)= \overrightarrow {m} \cdot \overrightarrow {n}$$, find the interval where $f(x)$ is monotonically increasing.

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