
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
Translate the graph of the function $y=5\sin \left( 2x+\dfrac{\pi}{4} \right)$ to the left by $\varphi$ units, where $0 < \varphi < \dfrac{\pi}{2}$, such that the resulting graph is symmetric about the $y$-axis. Find the value of $\varphi$.

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