
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 $$f(x)=\sin(2x+\varphi) \, (|\varphi| < \frac{\pi}{2})$$, if it is translated to the left by $$\frac{\pi}{3}$$ units and the resulting function is an even function, then $\varphi$ equals \_\_\_\_\_\_.

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