The Eastern Orthodox church and the Catholic church are two separate churches. The Eastern Orthodox church is not the same as the Eastern Rite Catholic churches, whose bishops are in union with the bishop of Rome.
The Catholic church views the leadership and the sacraments as valid, since they derive from apostolic authority and the Eastern Orthodox church can trace a valid succession all the way back to the Apostles (unlike Anglicanism, where at one point Anglicans clearly intended to no longer make Catholic priests and bishops, but to make Anglican priests and Bishops). As such, they are considered a true "Church", not a schismatic or heretical community.
A member of the Catholic church would be allowed to participate in all ways that would be considered honest ecumenism. There is no reason why one could not join with them to pray, sing, read scripture, attend a wedding or baptism, etc.
However, even though their sacraments are valid, it is not licit, or allowed, for a Catholic to participate in the sacraments of the Eastern Orthodox church. Primarily, this is because they are not a member of that community, and in the true spirit of ecumenism, a Catholic would not want to present themselves for Eucharist, for example, because the Eastern Orthodox churches may not always not intend to provide its sacraments to non-members.
Additionally, when Catholics receive Communion, they are expressing unity both with Christ and with the Catholic church. As a result, when a Catholic liturgy is available, this is understood as the proper place for Catholics to worship and receive.
However, when a Catholic liturgy is unavailable, a Catholic is permitted to attend services and receive in an Orthodox church. Ideally, the parishioner would seek the permission of both priests, to avoid any confusion, especially if the situation is not a one-time event.
So it depends on the nature of the participation. For example, if a Catholic is married to an Orthodox spouse, the Catholic would be allowed to attend and participate, but not communicate, in an Orthodox liturgy on a regular basis.