
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: $2x-1$ and $4x+3$ are two distinct square roots of $m$, and $2y+2$ is the integer part of $\sqrt{10}$.  
$(1)$ Find the values of $x$, $y$, and $m$.  
$(2)$ Find the square root of $1+4y$.

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