To answer major questions on supermassive black hole (SMBH) and galaxy evolution, a complete census of SMBH growth, i.e. active galactic nuclei (AGN), is required. Thanks to all-sky surveys by the Wide-field Infrared Survey Explorer (WISE) and the Spectrum-Roentgen-Gamma (SRG) missions, this task is now feasible in the nearby Universe. We present a new survey, the Local AGN Survey (LASr), with the goal of identifying AGN unbiased against obscuration and determining the intrinsic Compton-thick (CT) fraction. We construct the most complete all-sky galaxy sample within 100Mpc (90 per cent completeness for log(M_*_/M_{sun}_)~9.4), four times deeper than the current reference, the Two Micron All-Sky Survey Redshift Survey (2MRS), which misses ~20 per cent of known luminous AGN. These 49k galaxies serve as parent sample for LASr, called LASr-GPS. It contains 4.3k already known AGN, >=82 per cent of these are estimated to have L^nuc^(12{mu}m)<10^42.3^erg/s, i.e. are low-luminosity AGN. As a first method for identifying Seyfert-like AGN, we use WISE-based infrared colours, finding 221 galaxies at L^nuc^(12{mu}m)>=10^42.3^erg/s to host an AGN at 90 per cent reliability. This includes 61 new AGN candidates and implies an optical type 2 fraction of 50-71 per cent. We quantify the efficiency of this technique and estimate the total number of AGN with L^int^(2-10keV)>=10^42^erg/s in the volume to be 362^+145^_-116_ (8.6^+3.5^_-2.8_x10^-5^Mpc^-3^). X-ray brightness estimates indicate the CT fraction to be 40-55 per cent to explain the Swift non-detections of the infrared selected objects. One third of the AGN within 100 Mpc remain to be identified, and we discuss the prospects for the eROSITA all-sky survey to detect them.