
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
The graphs of  $y=3(x-h)^2+j$  and  $y=2(x-h)^2+k$  have  $y$ -intercepts of  $2013$  and  $2014$ , respectively, and each graph has two positive integer  $x$ -intercepts. Find  $h$ .

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