
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 $\overset{⇀}{a} =(\cos x,\sin x)$, $\overset{⇀}{b} =(-\cos x,\cos x)$, $\overset{⇀}{c} =(-1,0)$.

(1) If $x= \frac{π}{6}$, find the angle between vectors $\overset{⇀}{a}$ and $\overset{⇀}{c}$;

(2) When $x\in\left[\begin{matrix} \frac{π}{2}, \frac{9π}{8} \end{matrix}\right]$, find the maximum value of the function $f(x)=2 \overset{⇀}{a} \cdot \overset{⇀}{b} +1$ and the corresponding value of $x$.

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