
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
A circle $M$ with its center on the $x$-axis and a radius of $\sqrt{5}$ is located on the left side of the $y$-axis. It is tangent to the line $x + 2y = 0$. Determine the equation of circle $M$.

A) ${{(x-\sqrt{5})}^{2}}+{{y}^{2}}=5$
B) ${{(x+\sqrt{5})}^{2}}+{{y}^{2}}=5$
C) ${{(x-5)}^{2}}+{{y}^{2}}=5$
D) ${{(x+5)}^{2}}+{{y}^{2}}=5$

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