The letters A to J have been assigned values for 0 to 9 but not in that order.

G,I and C, not necessarily in that order, are increasingly consecutive digits as are F, B, J and A.
A 3-digit triangular number contains the values of A, C and F.
In some order E, G and J form two 3-digit squares while B, D and G treated similarly would yield three 3-digit squares.

1. Determine the values assigned to each letter.
2. Determine which sets of 6 letters may be arranged so that they form two 3-digit numbers where the values in one rise consecutively, those of the second decrease consecutively and their sum is a 4-digit palindrome.