Reduce[] sometimes solves inequalities I give it, sometimes it doesn't. Is there some general principles I'm missing or some common pitfalls I'm falling into?

For example, here is easy problem I can't seem to make MMa solve.

Reduce[{4*Abs[p + p^2] < 1, c == 1 - p - p^2}, p]

The hand-derived solution is just $|c-1|<\frac{1}{4}$ but MMa gets stuck.

Any pointers?

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    $\begingroup$ Sometimes it depends on the domain. If you add the option Reals, i.e. Reduce[{4*Abs[p + p^2] < 1, c == 1 - p - p^2}, p, Reals], it spits back an answer practically instantaneously. It is likely more difficult to solve that problem in the complex plane, which is what it assumes and probably why it gets stuck. $\endgroup$ – march Nov 27 '15 at 21:36
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    $\begingroup$ Or Reduce[{4*Abs[p + p^2] < 1, c == 1 - p - p^2, {c, p} \[Element] Reals}, {c}, {p}]... $\endgroup$ – Michael E2 Nov 27 '15 at 21:59

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