
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
The graph of the function $f(x)=\sin (2x+\varphi )$ $(|\varphi| < \frac{\pi}{2})$ is shifted to the left by $\frac{\pi}{6}$ units, and the resulting graph corresponds to an even function. Find the minimum value of $m$ such that there exists $x \in \left[ 0,\frac{\pi}{2} \right]$ such that the inequality $f(x) \leqslant m$ holds.

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