Learn Hardcore Japanese: atarasii taisaku wo kangaeru tame ni, syatyou to soudansimasita. - I consulted with the president to think of new measures.

Because ために attaches to the dictionary form of a verb to indicate purpose, i.e. “in order to do …”. The pattern is:
verb (dictionary form) + ために → “in order to (verb)”.
Here 考えるために means “in order to think up (measures)”.

Why is 考える in the dictionary form, and not 考えた or 考えます?

When you express purpose with ために, you must use the plain (dictionary) form of the verb.

考えるために = “in order to think”
If you said 考えたために, it would sound like “because I thought” (a cause, not a purpose).

What is the difference between ために and ための?

V(dictionary form) + ために = “in order to (verb)”. (marks purpose)
N + のために = “for the sake of N” or “for N’s benefit”. (also marks purpose but from a noun)
N + のための + N2 = “N2 for the purpose of N”. (noun modifying noun)

In our sentence we need “in order to think” so we use 考えるために, not 考えるための.

Why is 対策 followed by を?

Because 対策 is the direct object of the verb 考える. You “think up” or “come up with” something, so the thing you think of is marked with を.