
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 "Chinese Remainder Theorem," also known as the "Sunzi Theorem," was introduced to Europe by the British missionary Wiliam Alexander in 1852. In 1874, the British mathematician Mason pointed out that this method conforms to the general theorem on the solution of congruences obtained by Gauss in 1801. Therefore, it is known as the "Chinese Remainder Theorem" in the West. This theorem deals with the problem of divisibility. Now, among the numbers from 1 to 2023, all the numbers that leave a remainder of 1 when divided by 3 and a remainder of 1 when divided by 5 are arranged in ascending order to form a sequence $\{a_{n}\}$. The total number of terms in this sequence is ______.

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