
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 vectors $\overrightarrow{a}=(\sin x, \frac{3}{4})$, $\overrightarrow{b}=( \frac{1}{3}, \frac{1}{2}\cos x)$, $\overrightarrow{c}=( \frac{1}{6},\cos x)$, such that $\overrightarrow{a} \parallel (\overrightarrow{b}+ \overrightarrow{c})$, and $x \in (0, \frac{5π}{12})$, find the value of $x$.

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