
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
If  $ a,b,c\in {\rm Z}$  and
\[ \begin{array}{l} {x\equiv a\, \, \, \pmod{14}} 
{x\equiv b\, \, \, \pmod {15}} 
{x\equiv c\, \, \, \pmod {16}} \end{array}
\]
, calculate the number of integral solutions of the congruence system on the interval  $ 0\le x < 2000$.

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