
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
For the following system of equations and inequalities:
$$
\begin{array}{c}
x_{1}+x_{2}+x_{3}=15 \\
0 \leqslant x_{1} \leqslant 5, \quad 0 \leqslant x_{2} \leqslant 6, \quad 0 \leqslant x_{3} \leqslant 7
\end{array}
$$

Find the number of integer solutions.

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