I would recommend that they use both the "stick" and the "carrot" to fight crime. The "stick" included apprehending more criminals, punishing severely criminals who commit major crimes, and not punishing severely those who commit minor crimes. To apprehend more criminals, it is necessary to reform their corrupt-ridden police forces, partly through the creation of Internal Police Review Boards that focus on police corruption. The purpose of such Boards would be to punish police who engage in serious crimes, and penalize or dismiss police who do not try to catch criminals and protect against crimes.
The "carrot" partly means much higher pay for police. Their pay is now abysmally low in Mexico and many other countries, so that men and women attracted to becoming policemen expect to supplement their incomes by bribes and other corrupt acts. Good pay would attract more honest men and women to the police force. It would also raise the cost of dismissal to policemen for malfeasance since their best employment alternatives would then be far inferior to police earnings.
the problem is obvious, and so is the solution (better law enforcement). What they should study is why the Mexican government and other Latin American governments are incapable of implementing the obvious solution.
My guess is that inefficient government is an equilibrium outcome. The incentive for political leaders is probably to have a large number of low-paid government employees, to whom you can appeal for votes. It may be good public policy to trim the number of people on the government payroll while raising salaries to attract good workers who do not engage in bribery and kickbacks. However, this is not such good politics.