Do Catholics worship the Blessed Virgin Mary?

Some non-Catholics make the false claim that Catholics worship the Blessed Virgin Mary.

For this statement to be true, then the Church must be telling us to do this.
Therefore, if the Church is telling us to do this, then it must be written somewhere in official Catholic Church documents.

I have repeatedly asked the people who make this false charge to please show me the official written Catholic document which directs us to WORSHIP the Blessed Virgin.

The only reply I have ever received to that request was a quote from the Papal Encyclical 'Lumen Gentium':

LG 50. "...The Church has always believed that the Apostles and Christ's martyrs, who gave the supreme witness of faith and charity by the shedding of their blood, are closely united with us in Christ; she has always VENERATED them, together with the Blessed Virgin Mary and the holy angels, with a special love, and has asked piously for the help of their intercession."

Now, where in this quote does it say that Catholics WORSHIP the Blessed Virgin Mary?
The plain truth is that it does not say that unless you think to VENERATE someone, means to WORSHIP them.

The simple truth is that NOWHERE in Catholic literature will you ever find a document which directs Catholics to WORSHIP her. You will, however, find many documents which say we VENERATE her.

Here is what the dictionary says regarding the words venerate and worship:

Venerate: "To regard with respect, reverence, or heartfelt deference."
One of the 10 Commandments is "Honor your Father and your Mother." Do you honor your father and mother? Do you respect them? These are the things Catholics do for their parents, and for the Blessed Virgin Mary.

Worship: "The reverent love and devotion accorded a deity, an idol, or sacred object."
Do you worship your parents? Certainly not, and neither do Catholics worship theirs. However, it is perfectly alright to venerate them and for Catholics to venerate the Blessed Virgin Mary.

I would say the two words have quite different meanings wouldn't you? Why then, do some people continue to make this false charge?

I will ask again. Show me the official, authentic written Catholic document which directs Catholics to worship the Blessed Virgin Mary?