
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 $f(x) = \sin(\omega x + \frac{\pi}{4})$ ($\omega > 0$), the distance between two adjacent axes of symmetry of its graph is $\frac{\pi}{3}$.

(1) Find the analytical expression of the function $f(x)$.

(2) Find the smallest positive real number $m$, such that the graph of $f(x)$, when shifted to the left by $m$ units, corresponds to an even function.

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