
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

Solve the inequality \( x+2<\sqrt{x+14} \):

\[ 
(x+2<\sqrt{x+14}) \Leftrightarrow\left(\left[\begin{array}{l}
\left\{\begin{array}{l}
x+14 \geqslant 0 \\
x+2<0 \\
x+14 \geqslant 0 \\
x+2 \geqslant 0 \\
(x+2)^{2}<x+14
\end{array}\right.
\end{array}\right)\right. 
\]

By solving the combined system, the solution is \( [-14, 2) \). 

Next, let's consider a simpler method for solving these irrational inequalities, known as the interval method.

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