
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) = sinx + $\sqrt{3}$cosx + 1,
(1) Find the range of the function and the interval where the function is strictly increasing.
(2) If f(α) = $\frac{13}{5}$ and $\frac{π}{6}$ < α < $\frac{2π}{3}$, find the value of sin(2α + $\frac{2π}{3}$).

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