
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 the equation for \( x \):
\[ \sqrt{m-x^{2}}=\log _{2}(x+n) \]
when it has one positive and one negative real root, the range of values for \( n \) is \( 3 \leqslant n < 4 \). Determine the value of the constant \( m \).

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