
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
Determine how many integers satisfy the following inequalities:
\[
\begin{array}{cccc}
(1) & -4x & \geq & x+10 \\
(2) & -3x & \leq & 15 \\
(3) & -5x & \geq & 3x+24
\end{array}
\]

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