Instead of applying taxes and giving subsidies: How about removing both from Energy not just petroleum. Remove all taxes and levies from Petroleum. Then allow anybody who wants to import fuel to do so. He only has to show he has sufficient storage. That way the government has zero role in whether the price goes up or down.
About taxes: tax economic activities arising from the use of the energy. For instance if Pundit's uncle manufactures bricks using a concrete mixer and mould powered by a diesel Engine, tax the bricks but not the diesel.
Subsidies help nobody. If something is above the spending capacity of a citizen; let him not buy it. Eventually society settles on the reality of the new high costs.