
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 $f(x)=\cos^2 \omega x + \sqrt{3} \sin \omega x \cos \omega x + m (\omega > 0, m \in \mathbb{R})$, choose two out of the three conditions ①, ②, ③ that can determine the analytical expression of the function $f(x)$.<br/>Condition ①: The function $f(x)$ has a minimum positive period of $\pi$;<br/>Condition ②: The graph of the function $f(x)$ passes through the point $(0, \frac{1}{2})$;<br/>Condition ③: The maximum value of the function $f(x)$ is $\frac{3}{2}$.<br/>$(1)$ Find the analytical expression and the minimum value of $f(x)$;<br/>$(2)$ If the function $f(x)$ has exactly two axes of symmetry in the interval $[0, t]$ $(t > 0)$, find the range of values for $t$.

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