
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 $n \geq 2$, let \[
g_n(x) = g_{n-1}\left(\sqrt{5n^2 + x}\right).\]
Let $M$ be the largest value of $n$ for which the domain of $g_n$ 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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