
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 $\overrightarrow{a}=(\sin x,\cos x)$, $\overrightarrow{b}=(\sin x,\sin x)$, the function $f(x)=\overrightarrow{a}\cdot\overrightarrow{b}$.
1. Find the equation of the axis of symmetry for $f(x)$;
2. Find the interval where $f(x)$ is monotonically decreasing;
3. If for any real number $x \in \left[\frac{\pi}{6}, \frac{\pi}{3}\right]$, the inequality $f(x)-m < 2$ always holds, find the range of the real number $m$.

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