
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
Source: 2018 Canadian Open Math Challenge Part B Problem 4
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Determine the number of  $5$ -tuples of integers  $(x_1,x_2,x_3,x_4,x_5)$  such that $\text{(a)}$   $x_i\ge i$  for  $1\le i \le 5$ ; $\text{(b)}$   $\sum_{i=1}^5 x_i = 25$ .

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