Article 2 of the constitution states that the president is also

in the second paragraph of Article II, Section 2, that “the President shall have Power, by and with the Advice and Consent of the Senate to make Treaties, provided two thirds of the Senators present concur.” Thus, treaty making is a power shared between the President and the Senate.

Source: https://constitutioncenter.org/interactive-constitution/articles/article-ii

secretly cooperate with one another.

the constitution of the united states gave congress the absolute authority over immigration laws