
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
Let $g_{1}(x)=\sqrt{4-x}$, and for integers $m \geq 2$, let \[g_{m}(x)=g_{m-1}\left(\sqrt{(m+1)^2 - x}\right).\] Let $M$ be the largest value of $m$ for which the domain of $g_m$ is nonempty. For this value of $M,$ the domain of $g_M$ consists of a single point $\{d\}.$ Compute $d.$

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