
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) = msin(2x) - cos^2(x) - $\frac{1}{2}$, where x ∈ R, and if tanα = 2$\sqrt{3}$ and f(α) = -$\frac{3}{26}$.
1. Find the value of the real number m and the smallest positive period of the function f(x).
2. Find the increasing interval of f(x) on [0, π].

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