
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 $f(x) = \sin 2x$ such that all points on its graph are shifted to the right by $\dfrac{\pi}{4}$ units to obtain the graph of the function $g(x)$, determine the maximum value of $a$ for which $g(x)$ is monotonically increasing on the interval $[0, a]$.

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