
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 a function $f(x)$ on the interval $[a,b]$, if there exists an $x\_0∈[a,b]$ such that $f(x\_0)=∫_a^bf(x)dx$, then $x\_0$ is called an "integral point" of the function $f(x)$ on the interval $[a,b]$. Find the "integral point" of the function $f(x)=cos(2x+π/6)$ on the interval $[0,π/2]$.

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