Step 1: Recall definition of reducing agent.
A reducing agent is the substance that undergoes oxidation by losing electrons.
Step 2: Analyze oxidation states.
In \(\mathrm{CH_4}\), carbon has oxidation state \(-4\).
In \(\mathrm{CO_2}\), carbon has oxidation state \(+4\).
Step 3: Identify the oxidized species.
Carbon in methane is oxidized from \(-4\) to \(+4\), hence methane undergoes oxidation.
Step 4: Conclusion.
Therefore, \(\mathrm{CH_4}\) acts as the reducing agent in the reaction.