
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 "Han Xin's Troop Counting" problem has many interesting names in the history of ancient Chinese mathematics, such as "Counting without Knowing the Number," "Guiguzi's Calculation," "Wall Separation Calculation," "Dayan's Method for Seeking Unity," etc. Among them, the solution to the "Counting without Knowing the Number" problem in the "Sunzi's Arithmetic Classic" was not introduced to Europe until 1852 by missionaries. It was later verified to conform to a general theorem on the solution of congruences developed by Gauss, hence the West named it the "Chinese Remainder Theorem." The original text goes as follows: "Now there is an unknown number of items. When counted in threes, two remain; when counted in fives, three remain; when counted in sevens, two remain. What is the number of items?" This is a problem where a certain number leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a remainder of 2 when divided by 7, and the task is to find this number. If we list all the numbers from 1 to 2018 that satisfy these conditions in ascending order, the median of this sequence is ______.

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