
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 $f(x)=\tan({ωx+φ})({ω≠0,|φ|＜\frac{π}{2}})$, points $({\frac{π}{3},0})$ and $({\frac{{5π}}{6},0})$ are two adjacent symmetric centers of the function. It is monotonically decreasing in the interval $({\frac{π}{3},\frac{{2π}}{3}})$. Find the value of $\varphi$.

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