Both Uses

reflect
in
The Necklace, by Guy de Maupassant
(Edited)

She reflected several seconds, making her calculations and wondering also what sum she could ask without drawing on herself an immediate refusal and a frightened exclamation from the economical clerk.
*

reflected = thought carefully
As to him, he reflected that he must be at the ministry at ten o'clock that morning.

Definitions:

(1) (reflect as in: reflect in the mirror)
show an image back (on a mirror or other shiny surface)
(2) (reflect as in: reflect American Values)
to show something -- such as to demonstrate, express, or represent
The exact meaning of this sense of reflect depends upon its context. For example:
- "She says the immorality in the movie reflects American values." -- expresses or represents
- "It reflects the selfishness she had seen growing for years." -- demonstrates
- "She did not reflect the panic that surrounded her." -- demonstrate or show indication of
(3) (reflect as in: I want to reflect on it.)
think carefully -- possibly aloud or in writing
(4) (reflect as in: reflect poorly on the school)
influence opinion

This word is often used in a phrase like "reflect poorly on/upon...." Although we define this meaning of reflect as "influence opinion", the use of "upon" or "on" might feel more natural if you think of it as "casting a shade of good or bad upon/on" something.
(5) (reflect as in: reflect the light/heat/sound)
bounce back (rather than absorbing)
(6) (meaning too rare to warrant focus)
See a comprehensive dictionary for less common meanings of reflect.