Solution

$L_1={a^n b^n c^m}\cup{a^n b^m c^m}$ is a standard example of an inherently ambiguous language.

Reason: strings of the form $a^n b^n c^n$ can be generated from both parts:

First part: $a^n b^n c^m$ when $m=n$

Second part: $a^n b^m c^m$ when $m=n$

So, ambiguity is unavoidable for $L_1$.

Now,

$L_2={ww^R\mid w\in{a,b}^*}$ is the language of even length palindromes.

This language is context-free and not inherently ambiguous.