
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 $\overset{⇀}{a}=(\sin x,\cos x)$ and $\overset{⇀}{b}=(\sin x,\sin x)$, the function $f(x)$ is defined as $f(x) = \overset{⇀}{a} \cdot \overset{⇀}{b}$.

1. Find the equation of the axis of symmetry for $f(x)$;
2. Find the set of all $x$ values that satisfy $f(x) \geq 1$;
3. If the inequality $f(x) - m < 2$ holds true for any real number $x \in [\frac{π}{6}, \frac{π}{3}]$, find the range of values for the real number $m$.

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