
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 that $f(x) = \sin{2x} + \sqrt{3}\cos{2x}$ ($x \in \mathbb{R}$).

1. Find the value of $f(\frac{5\pi}{6})$.
2. If $x \in [0, \frac{\pi}{4}]$, find the range of the function $f(x)$.

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