
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 $y=\sin 2x$ along the $x$-axis to the left by $\dfrac{\pi }{6}$ units, and stretch the ordinate to twice its original length (the abscissa remains unchanged) to obtain the graph of the function $y=f(x)$. If the minimum value of the function $y=f(x)+a$ on the interval $\left[ 0,\dfrac{\pi }{2} \right]$ is $\sqrt{3}$, then $a=\boxed{\_\_\_\_\_}$.

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