
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
How many integer solutions are there to the equation \( x_{1} + x_{2} + x_{3} + x_{4} = 18 \) satisfying \( 1 \leq x_{1} \leq 5 \), \( -2 \leq x_{2} \leq 4 \), \( 0 \leq x_{3} \leq 5 \), and \( 3 \leq x_{4} \leq 9 \)?

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