
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 $f(x)=\tan(\omega x + \phi)$ $(\omega \neq 0, \left|\phi\right| < \frac{\pi}{2})$, points $\left(\frac{2\pi}{3}, 0\right)$ and $\left(\frac{7\pi}{6}, 0\right)$ are two adjacent centers of symmetry for $f(x)$, and the function is monotonically decreasing in the interval $\left(\frac{2\pi}{3}, \frac{4\pi}{3}\right)$, find the value of $\phi$.

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