
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 that the function $f(x) = \begin{cases} (x-a)^2, & x\leqslant 0 \\ x+\frac{1}{x}+a, & x>0 \end{cases}$ attains its minimum value at $x=0$, find the maximum value of $a$.
A) $1$
B) $2$
C) $3$
D) $4$

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